If A and B are two events such that P(A) andne; 0 and P(B - A) = 1, thena)B andsub; Ab)B = c)A andsub; Bd)None of theseCorrect answer is option 'C'. Can you explain this answer?

EduRev

All Courses

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

ACT Exam > ACT Questions > If A and B are two events such that P(A) ≠...

If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, then

a)
B ⊂ A
b)
B = ϕ
c)
A ⊂ B
d)
None of these

Correct answer is option 'C'. Can you explain this answer?

Join for Free

Join for Free

Verified Answer

If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, then...

Concept:

P(A|B) = P(A∩B)/P(B)
P(B|A) = P(A∩B)/P(A)
A ⊂ B = Proper Subset: every element of A is in B, but B has more elements.
ϕ = Empty set = {}

Calculation:

Given: P(B/A) = 1

⇒ P(B|A) = P(A∩B)/P(A) = 1

⇒ P(A ∩ B) = P(A)

⇒ (A ∩ B) = A

So, every element of A is in B, but B has more elements.

∴ A ⊂ B

View all questions of this test

Most Upvoted Answer

If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, then...

Concept:

P(A|B) = P(A∩B)/P(B)
P(B|A) = P(A∩B)/P(A)
A ⊂ B = Proper Subset: every element of A is in B, but B has more elements.
ϕ = Empty set = {}

Calculation:

Given: P(B/A) = 1

⇒ P(B|A) = P(A∩B)/P(A) = 1

⇒ P(A ∩ B) = P(A)

⇒ (A ∩ B) = A

So, every element of A is in B, but B has more elements.

∴ A ⊂ B

Answered by Orion Classes · View profile

Free Test

FREE

Test: Probability - 3
15 Ques | 25 Min

Start Free Test

View all free ACT tests

Community Answer

If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, then...

Concept:

P(A|B) = P(A∩B)/P(B)
P(B|A) = P(A∩B)/P(A)
A ⊂ B = Proper Subset: every element of A is in B, but B has more elements.
ϕ = Empty set = {}

Calculation:

Given: P(B/A) = 1

⇒ P(B|A) = P(A∩B)/P(A) = 1

⇒ P(A ∩ B) = P(A)

⇒ (A ∩ B) = A

So, every element of A is in B, but B has more elements.

∴ A ⊂ B

View all answers Start learning for free

Explore Courses for ACT exam

Similar ACT Doubts

A and B are two events such that P(B) = 0.4 and P(A ∪ B) = 0.6 If A and B are independent, then P(

View answer

Directions:In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will ﬁnd alternatives for the words and phrases that are underlined. If you think that the original version is best, choose “NO CHANGE,”. You will also ﬁnd questions about a particular section of the passage, or about the entire passage. These questions will be identiﬁed either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer.PassageA Gift From the HeartContrary to advertisements seen on(1)television, read, in magazines,or heard on the radio, (2)having spent a lot of moneyon a gift for a friend or loved one is totally unnecessary. (3)Many people collect photos or mementos from special events, trips, or celebrations throughout their lives, throwing them in a drawer or cardboard box somewhere, intending to sort them out later. It seems, though, that “later” never comes. So, the next time (4)you’re readyto plop down a plastic credit card for a silk scarf or pair of leather gloves for that special someone (5) whom you care about, consider sorting through that junk drawer (6)ﬁlled oftrinkets and special photos.1. For example, you can decorate an inexpensive picture frame with colorful buttons for your seamstress mother, or (7)you can usenuts and bolts for your workshop-crazed brother.2.Shadow boxes are also a wonderful way to display several objects from a single special event, such as a wedding.3. Inserting a special photo of you and that certain someone will create a gift that will be treasured forever.4. Take the original wedding invitation, a candy favor, (8)and a dried ﬂower from the table centerpiece, a napkin, or anything else that you can (9)gather fromthe wedding.(10)When you have many photos and (11)mementos, makinga photo album or scrapbook for a friend or family member. Today, the options for embellishing your book (12)are near to be endless. Entering a scrapbooking store can make your head spin. If (13)somehappens to you on your ﬁrst scrapbooking venture, consider taking an introductoryclass, which many stores offer. (14)Of course, you will have a much better idea of which scrapbook supplies to buy when the class ends.Pictures or books that can be enjoyed over and over again are one-of-a-kind, original gifts. There is nothing like receiving a gift that comes straight from the heart. Such gifts help people recall happy times and solidify the bond between the giver and the receiver.(15)Q. (5)

View answer

Directions:In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will ﬁnd alternatives for the words and phrases that are underlined. If you think that the original version is best, choose “NO CHANGE,”. You will also ﬁnd questions about a particular section of the passage, or about the entire passage. These questions will be identiﬁed either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer.PassageA Gift From the HeartContrary to advertisements seen on(1)television, read, in magazines,or heard on the radio, (2)having spent a lot of moneyon a gift for a friend or loved one is totally unnecessary. (3)Many people collect photos or mementos from special events, trips, or celebrations throughout their lives, throwing them in a drawer or cardboard box somewhere, intending to sort them out later. It seems, though, that “later” never comes. So, the next time (4)you’re readyto plop down a plastic credit card for a silk scarf or pair of leather gloves for that special someone (5) whom you care about, consider sorting through that junk drawer (6)ﬁlled oftrinkets and special photos.1. For example, you can decorate an inexpensive picture frame with colorful buttons for your seamstress mother, or (7)you can usenuts and bolts for your workshop-crazed brother.2.Shadow boxes are also a wonderful way to display several objects from a single special event, such as a wedding.3. Inserting a special photo of you and that certain someone will create a gift that will be treasured forever.4. Take the original wedding invitation, a candy favor, (8)and a dried ﬂower from the table centerpiece, a napkin, or anything else that you can (9)gather fromthe wedding.(10)When you have many photos and (11)mementos, makinga photo album or scrapbook for a friend or family member. Today, the options for embellishing your book (12)are near to be endless. Entering a scrapbooking store can make your head spin. If (13)somehappens to you on your ﬁrst scrapbooking venture, consider taking an introductoryclass, which many stores offer. (14)Of course, you will have a much better idea of which scrapbook supplies to buy when the class ends.Pictures or books that can be enjoyed over and over again are one-of-a-kind, original gifts. There is nothing like receiving a gift that comes straight from the heart. Such gifts help people recall happy times and solidify the bond between the giver and the receiver.(15)Q. (3)

View answer

Directions:In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will ﬁnd alternatives for the words and phrases that are underlined. If you think that the original version is best, choose “NO CHANGE,”. You will also ﬁnd questions about a particular section of the passage, or about the entire passage. These questions will be identiﬁed either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer.PassageA Gift From the HeartContrary to advertisements seen on(1)television, read, in magazines,or heard on the radio, (2)having spent a lot of moneyon a gift for a friend or loved one is totally unnecessary. (3)Many people collect photos or mementos from special events, trips, or celebrations throughout their lives, throwing them in a drawer or cardboard box somewhere, intending to sort them out later. It seems, though, that “later” never comes. So, the next time (4)you’re readyto plop down a plastic credit card for a silk scarf or pair of leather gloves for that special someone (5) whom you care about, consider sorting through that junk drawer (6)ﬁlled oftrinkets and special photos.1. For example, you can decorate an inexpensive picture frame with colorful buttons for your seamstress mother, or (7)you can usenuts and bolts for your workshop-crazed brother.2.Shadow boxes are also a wonderful way to display several objects from a single special event, such as a wedding.3. Inserting a special photo of you and that certain someone will create a gift that will be treasured forever.4. Take the original wedding invitation, a candy favor, (8)and a dried ﬂower from the table centerpiece, a napkin, or anything else that you can (9)gather fromthe wedding.(10)When you have many photos and (11)mementos, makinga photo album or scrapbook for a friend or family member. Today, the options for embellishing your book (12)are near to be endless. Entering a scrapbooking store can make your head spin. If (13)somehappens to you on your ﬁrst scrapbooking venture, consider taking an introductoryclass, which many stores offer. (14)Of course, you will have a much better idea of which scrapbook supplies to buy when the class ends.Pictures or books that can be enjoyed over and over again are one-of-a-kind, original gifts. There is nothing like receiving a gift that comes straight from the heart. Such gifts help people recall happy times and solidify the bond between the giver and the receiver.(15)Q. (14)Given that all of the choices are true, which one would best conclude the paragraph while providing the reader with the most speciﬁc and detailed information about why store owners offer introductory classes?

View answer

Directions:In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will ﬁnd alternatives for the words and phrases that are underlined. If you think that the original version is best, choose “NO CHANGE,”. You will also ﬁnd questions about a particular section of the passage, or about the entire passage. These questions will be identiﬁed either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer.PassageA Gift From the HeartContrary to advertisements seen on(1)television, read, in magazines,or heard on the radio, (2)having spent a lot of moneyon a gift for a friend or loved one is totally unnecessary. (3)Many people collect photos or mementos from special events, trips, or celebrations throughout their lives, throwing them in a drawer or cardboard box somewhere, intending to sort them out later. It seems, though, that “later” never comes. So, the next time (4)you’re readyto plop down a plastic credit card for a silk scarf or pair of leather gloves for that special someone (5) whom you care about, consider sorting through that junk drawer (6)ﬁlled oftrinkets and special photos.1. For example, you can decorate an inexpensive picture frame with colorful buttons for your seamstress mother, or (7)you can usenuts and bolts for your workshop-crazed brother.2.Shadow boxes are also a wonderful way to display several objects from a single special event, such as a wedding.3. Inserting a special photo of you and that certain someone will create a gift that will be treasured forever.4. Take the original wedding invitation, a candy favor, (8)and a dried ﬂower from the table centerpiece, a napkin, or anything else that you can (9)gather fromthe wedding.(10)When you have many photos and (11)mementos, makinga photo album or scrapbook for a friend or family member. Today, the options for embellishing your book (12)are near to be endless. Entering a scrapbooking store can make your head spin. If (13)somehappens to you on your ﬁrst scrapbooking venture, consider taking an introductoryclass, which many stores offer. (14)Of course, you will have a much better idea of which scrapbook supplies to buy when the class ends.Pictures or books that can be enjoyed over and over again are one-of-a-kind, original gifts. There is nothing like receiving a gift that comes straight from the heart. Such gifts help people recall happy times and solidify the bond between the giver and the receiver.(15)Q. (4)

View answer

Top Courses for ACTView all

Top Courses for ACT

View all

If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer?.

Solutions for If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for ACT. Download more important topics, notes, lectures and mock test series for ACT Exam by signing up for free.

Here you can find the meaning of If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice ACT tests.

Explore Courses for ACT exam