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Assertion & Reason Test: Probability - 1 - Class 10 MCQ


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10 Questions MCQ Test - Assertion & Reason Test: Probability - 1

Assertion & Reason Test: Probability - 1 for Class 10 2024 is part of Class 10 preparation. The Assertion & Reason Test: Probability - 1 questions and answers have been prepared according to the Class 10 exam syllabus.The Assertion & Reason Test: Probability - 1 MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Assertion & Reason Test: Probability - 1 below.
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Assertion & Reason Test: Probability - 1 - Question 1

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Let A and B be two independent events.

Assertion : If P (A) = 0.3 and P (A ∪ ) = 0.8, then P (B) is 2/7.

Reason : P ( ) = 1 - P(E), where E is any event.

Detailed Solution for Assertion & Reason Test: Probability - 1 - Question 1
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

P(A∪B′) = P(A) + P(B′) − P(A)P(B′)

∴ 0.8 = 0.3 + P(B′) − 0.3P(B′)

⇒ 0.5 = P(B′)(0.7)

⇒ P(B′) = 57

∴ P(B) = 1 − 57

= 2/7

Assertion & Reason Test: Probability - 1 - Question 2

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : When two coins are tossed simultaneously then the probability of getting no tail is 1/4.

Reason : The probability of getting a head (i.e., no tail) in one toss of a coin is 1/2.

Detailed Solution for Assertion & Reason Test: Probability - 1 - Question 2
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Probability of getting no tail when two coins tossed simultaneously i.e., both are heads.

Probability of both head

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Assertion & Reason Test: Probability - 1 - Question 3

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion: If the probability of an event is P then probability of its complementary event will be 1 - P.

Reason: When E and are complementary events, then P (E) + P( ) = 1.

Detailed Solution for Assertion & Reason Test: Probability - 1 - Question 3
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Both statements are correct and Reason is the correct for Assertion.

Since, probability of an event + probability of its complementary event = 1

So, probability of its complementary event = (1 – Probability of an event) = 1 – P.

Assertion & Reason Test: Probability - 1 - Question 4

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : In a simultaneous throw of a pair of dice. The probability of getting a double is 1/6.

Reason: Probability of an event may be negative.

Detailed Solution for Assertion & Reason Test: Probability - 1 - Question 4
Assertion (A) is true but reason (R) is false. When two dice are tossed. Total possible outcomes = 36

n(S) = 36

and total favourable outcomes (doublet)

= {(1,1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}

n (E) = 6

Probability = 6/36 = 1/6 and, we know that 0 ≤ P(E) ≤ 1.

Assertion & Reason Test: Probability - 1 - Question 5

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : The probability of winning a game is 0.4, then the probability of losing it, is 0.6

Reason : P(E) + P(not E) = 1

Detailed Solution for Assertion & Reason Test: Probability - 1 - Question 5
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

We have, P(E) = 0.4,

where E = event of winning

P(Not E) = 1 - P(E) = 1 - 0.4 = 0.6

Assertion & Reason Test: Probability - 1 - Question 6

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : Cards numbered as 1, 2, 3 .......... 15 are put in a box and mixed thoroughly, one card is then drawn at random. The probability of drawing an even number is 1/2.

Reason : For any event E, we have 0 ≤ P(E) ≤ 1

Detailed Solution for Assertion & Reason Test: Probability - 1 - Question 6
Assertion (A) is false but reason (R) is true. Total possible outcomes = 15

n(S) = 15

Total favourable numbers are 2, 4, 6, 8, 10, 12, 14.

E = {2, 4, 6, 8, 10, 12, 14}

n(E) = 7

Probability of drawing an even number = 7/15

Assertion & Reason Test: Probability - 1 - Question 7

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : If E and F are events such that P(E) = 1/4, P(F) = 1/2 and P(E and F) = 1/8, then P (E or F) is 5/8.

Reason : If A and B are independent, then P (A ∩ B) = P (A).

Detailed Solution for Assertion & Reason Test: Probability - 1 - Question 7
Assertion (A) is true but reason (R) is false.

P (E or F) = P (E ∪ F)

= P(E) + P(F) - P(E ∩ F)

= 1/4 + 1/2 - 1/8 = 5/8

Assertion & Reason Test: Probability - 1 - Question 8

Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion: The probabilities that A, B, C can solve a problem independently are 1/3, 1/3 and 1/4 respectively. The probability that only two of them are able to solve the problem is 7/36.

Reason : If A and B are mutually exclusive events, then P(A ∩ B) ≠ 0.

Detailed Solution for Assertion & Reason Test: Probability - 1 - Question 8
Assertion (A) is true but reason (R) is false.

1. A and B solve the problem and C does not solve the problem

2. B and C solve the problem and A does not solve the problem and

3. C and A solve the problem and B does not solve the problem. The required probability

Assertion & Reason Test: Probability - 1 - Question 9

Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): If P(F) = 0.20, then the probability of ‘not E’ is 0.80.

Reason (R): If two dice are thrown together, then the probability of getting a doublet is 5/6.

Detailed Solution for Assertion & Reason Test: Probability - 1 - Question 9
In case of assertion

P(E) = 0.20

∴ P(not E) = 1 – P(E)

= 1 – 0.20

= 0.80

∴ Assertion is correct.

In case of reason:

Total number of possible outcomes = 62 = 36

E : (doublets are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

No. of favourable outcomes to E = 6

∴ P(a doublet)

= Number of outcomes favourable to E/Total number of outcomes

= 6/36 = 1/6

∴ Reason is incorrect:

Hence, the assertion is correct but the reason is incorrect.

Assertion & Reason Test: Probability - 1 - Question 10

Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): The probability that a number selected at random from the number 1, 2, 3, ......., 15 is a multiple of 4, is 1/3.

Reason (R): Two different coins are tossed simultaneously. The probability of getting at least one head is 3/4.

Detailed Solution for Assertion & Reason Test: Probability - 1 - Question 10
In case of assertion

n(S) = 15

n(A) = 3

p(A) = n(A)/n(S) = 3/15 = 1/5.

∴ Assertion is incorrect.

In case of reason:

S = HH, HT, TH, TT

A = HH, HT, TH

n(S) = 4

n(A) = 3

∴ p(A) = n(A)/n(S) = 3/4.

∴ Reason is correct:

Hence, the assertion is incorrect but the reason is correct.

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