Test: Probability- Case Based Type Questions- 1 - JEE MCQ

# Test: Probability- Case Based Type Questions- 1 - JEE MCQ

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## 15 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Probability- Case Based Type Questions- 1

Test: Probability- Case Based Type Questions- 1 for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Probability- Case Based Type Questions- 1 questions and answers have been prepared according to the JEE exam syllabus.The Test: Probability- Case Based Type Questions- 1 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Probability- Case Based Type Questions- 1 below.
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Test: Probability- Case Based Type Questions- 1 - Question 1

### Direction: Read the following text and answer the following questions on the basis of the same:Anand, Samanyu and Shah of SHORTCUTS classes were given a problem in Mathematics whose respective probabilities of solving it are 1/2 , 1/3 and 1/4. They were asked to solve it independently.Based on the above data, answer any four of the following questions.Q. The probability that exactly one of them solves it is _______.

Detailed Solution for Test: Probability- Case Based Type Questions- 1 - Question 1
P(A ∩ B′ ∩ C′) + P(A′ ∩ B ∩ C′) + P(A′ ∩ B′ ∩ C)

= P(A) P(B′) P(C′) + P(A′) P(B) P(C′) + P(A′) P(B′) P(C)

= 11/24

Test: Probability- Case Based Type Questions- 1 - Question 2

### Direction: Read the following text and answer the following questions on the basis of the same:Anand, Samanyu and Shah of SHORTCUTS classes were given a problem in Mathematics whose respective probabilities of solving it are 1/2 , 1/3 and 1/4. They were asked to solve it independently.Based on the above data, answer any four of the following questions.Q. The probability that the problem is not solved is _______.

Detailed Solution for Test: Probability- Case Based Type Questions- 1 - Question 2
P(A′ ∩ B′ ∩ C′) = P(A′) P(B′) P(C′)

= 1/4.

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Test: Probability- Case Based Type Questions- 1 - Question 3

### Direction: Read the following text and answer the following questions on the basis of the same:Anand, Samanyu and Shah of SHORTCUTS classes were given a problem in Mathematics whose respective probabilities of solving it are 1/2 , 1/3 and 1/4. They were asked to solve it independently.Based on the above data, answer any four of the following questions.Q. The probability that Anand alone solves it is _______.

Detailed Solution for Test: Probability- Case Based Type Questions- 1 - Question 3
Let A → event that Anand solves

B → event that Samanyu solves

C → event that Shah solves

Test: Probability- Case Based Type Questions- 1 - Question 4

Direction: Read the following text and answer the following questions on the basis of the same:

Anand, Samanyu and Shah of SHORTCUTS classes were given a problem in Mathematics whose respective probabilities of solving it are 1/2 , 1/3 and 1/4. They were asked to solve it independently.

Q. The probability that the problem is solved is _______.

Detailed Solution for Test: Probability- Case Based Type Questions- 1 - Question 4
P(A ∪ B ∪ C) = 1 – P(A′) P(B′) P(C′)

= 3/4

Test: Probability- Case Based Type Questions- 1 - Question 5

Direction: Read the following text and answer the following questions on the basis of the same:

Anand, Samanyu and Shah of SHORTCUTS classes were given a problem in Mathematics whose respective probabilities of solving it are 1/2 , 1/3 and 1/4. They were asked to solve it independently.

Q. The probability that exactly two of them solves it is _______.

Detailed Solution for Test: Probability- Case Based Type Questions- 1 - Question 5
P(A ∩ B ∩ C′) + P(A ∩ B′ ∩ C) + P(A′ ∩ B ∩ C)

= P(A) P(B) P(C′) + P(A) P(B′) P(C) + P (A′) P(B) P(C)

= 6/24

= 1/4

Test: Probability- Case Based Type Questions- 1 - Question 6

Direction: Read the following text and answer the following questions on the basis of the same:

In an office three employees Vinay, Sonia and Iqbal process incoming copies of a certain form. Vinay process 50% of the forms. Sonia processes 20% and Iqbal the remaining 30% of the forms. Vinay has an error rate of 0.06, Sonia has an error rate of 0.04 and Iqbal has an error rate of 0.03.

Q. The manager of the company wants to do a quality check. During inspection he selects a form at random from the days output of processed forms. If the form selected at random has an error, the probability that the form is NOT processed by Vinay is :

Test: Probability- Case Based Type Questions- 1 - Question 7

Direction: Read the following text and answer the following questions on the basis of the same:

In an office three employees Vinay, Sonia and Iqbal process incoming copies of a certain form. Vinay process 50% of the forms. Sonia processes 20% and Iqbal the remaining 30% of the forms. Vinay has an error rate of 0.06, Sonia has an error rate of 0.04 and Iqbal has an error rate of 0.03.

Q. The probability that Sonia processed the form and committed an error is :

Detailed Solution for Test: Probability- Case Based Type Questions- 1 - Question 7
P (sonia processed the form and committed an error) = 20% × 0.4

Test: Probability- Case Based Type Questions- 1 - Question 8

Direction: Read the following text and answer the following questions on the basis of the same:

In an office three employees Vinay, Sonia and Iqbal process incoming copies of a certain form. Vinay process 50% of the forms. Sonia processes 20% and Iqbal the remaining 30% of the forms. Vinay has an error rate of 0.06, Sonia has an error rate of 0.04 and Iqbal has an error rate of 0.03.

Q. The conditional probability that an error is committed in processing given that Sonia processed the form is :

Test: Probability- Case Based Type Questions- 1 - Question 9

Direction: Read the following text and answer the following questions on the basis of the same:

In an office three employees Vinay, Sonia and Iqbal process incoming copies of a certain form. Vinay process 50% of the forms. Sonia processes 20% and Iqbal the remaining 30% of the forms. Vinay has an error rate of 0.06, Sonia has an error rate of 0.04 and Iqbal has an error rate of 0.03.

Q. The total probability of committing an error in processing the form is :

Test: Probability- Case Based Type Questions- 1 - Question 10

Direction: Read the following text and answer the following questions on the basis of the same:

In an office three employees Vinay, Sonia and Iqbal process incoming copies of a certain form. Vinay process 50% of the forms. Sonia processes 20% and Iqbal the remaining 30% of the forms. Vinay has an error rate of 0.06, Sonia has an error rate of 0.04 and Iqbal has an error rate of 0.03.

Q. Let A be the event of committing an error in processing the form and let E1, E2 and E3 be the events that Vinay, Sonia and Iqbal processed the form. The value of

Detailed Solution for Test: Probability- Case Based Type Questions- 1 - Question 10

[∵ sum of all occurrence of an event is equal to 1]

Test: Probability- Case Based Type Questions- 1 - Question 11

Direction: Read the following text and answer the following questions on the basis of the same:

The reliability of a COVID PCR test is specified as follows:

Of people having COVID, 90% of the test detects the disease but 10% goes undetected. Of people free of COVID, 99% of the test is judged COVID negative but 1% are diagnosed as showing COVID positive. From a large population of which only 0.1% have COVID, one person is selected at random, given the COVID PCR test, and the pathologist reports him/ her as COVID positive.

Q. What is the probability that the ‘person is actually having COVID given that ‘he is tested as COVID positive’?

Detailed Solution for Test: Probability- Case Based Type Questions- 1 - Question 11

Test: Probability- Case Based Type Questions- 1 - Question 12

Direction: Read the following text and answer the following questions on the basis of the same:

The reliability of a COVID PCR test is specified as follows:

Of people having COVID, 90% of the test detects the disease but 10% goes undetected. Of people free of COVID, 99% of the test is judged COVID negative but 1% are diagnosed as showing COVID positive. From a large population of which only 0.1% have COVID, one person is selected at random, given the COVID PCR test, and the pathologist reports him/ her as COVID positive.

Q. What is the probability of the ‘person to be tested as COVID positive’ given that ‘he is actually not having COVID’?

Detailed Solution for Test: Probability- Case Based Type Questions- 1 - Question 12
Probability of person to be tested as Covid positive given that he is actually not having Covid = P(G/E)= 1% = 1/100 = 0.01
Test: Probability- Case Based Type Questions- 1 - Question 13

Direction: Read the following text and answer the following questions on the basis of the same:

The reliability of a COVID PCR test is specified as follows:

Of people having COVID, 90% of the test detects the disease but 10% goes undetected. Of people free of COVID, 99% of the test is judged COVID negative but 1% are diagnosed as showing COVID positive. From a large population of which only 0.1% have COVID, one person is selected at random, given the COVID PCR test, and the pathologist reports him/ her as COVID positive.

Q. What is the probability of the ‘person to be tested as COVID positive’ given that ‘he is actually having COVID’?

Detailed Solution for Test: Probability- Case Based Type Questions- 1 - Question 13
E = Person selected has Covid

F = Does not have Covid

G = Test judge Covid positive

Probability of the person to be tested as Covid positive given that he is actually having Covid

Test: Probability- Case Based Type Questions- 1 - Question 14

Direction: Read the following text and answer the following questions on the basis of the same:

The reliability of a COVID PCR test is specified as follows:

Of people having COVID, 90% of the test detects the disease but 10% goes undetected. Of people free of COVID, 99% of the test is judged COVID negative but 1% are diagnosed as showing COVID positive. From a large population of which only 0.1% have COVID, one person is selected at random, given the COVID PCR test, and the pathologist reports him/ her as COVID positive.

Q. What is the probability that the ‘person is actually not having COVID’?

Detailed Solution for Test: Probability- Case Based Type Questions- 1 - Question 14
P(E) = 1 - P(E)

= 0.999

Test: Probability- Case Based Type Questions- 1 - Question 15

Direction: Read the following text and answer the following questions on the basis of the same:

The reliability of a COVID PCR test is specified as follows:

Of people having COVID, 90% of the test detects the disease but 10% goes undetected. Of people free of COVID, 99% of the test is judged COVID negative but 1% are diagnosed as showing COVID positive. From a large population of which only 0.1% have COVID, one person is selected at random, given the COVID PCR test, and the pathologist reports him/ her as COVID positive.

Q. What is the probability that the ‘person selected will be diagnosed as COVID positive’?

Detailed Solution for Test: Probability- Case Based Type Questions- 1 - Question 15

The probability that the person selected will be diagnosed as COVID positive is 0.01089.

To find this probability, we can use Bayes' theorem, which states that:

P(A|B) = P(B|A) * P(A) / P(B)

Where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring.

In this case, we are trying to find the probability that the person selected has COVID given that they have tested positive, so P(A|B) is the probability we are trying to find.

We are given that P(B|A) = 90% (the probability that the test will detect COVID given that the person has COVID), P(A) = 0.1% (the probability that the person selected has COVID), and P(B) = (0.1% * 90%) + (99.9% * 1%) = 0.1089 (the probability that the person will test positive).

Substituting these values into Bayes' theorem, we get:

P(A|B) = (90%) * (0.1%) / (0.1089) = 0.01089

Therefore, the probability that the person selected will be diagnosed as COVID positive is 0.01089.

## Mathematics (Maths) Class 12

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## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests