Question

1. Assertion (A): If a pair of dice is thrown once, then the probability of getting a sum of 8 is 5/36.
Reason (R): In a simultaneous toss of two coins, the probability of getting exactly one head is 1/2.
a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
c) Assertion(A) is true but reason (R) is false
d) Assertion(A) is false but reason (R) is true​

Answer 1

Answer:

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Answer 2

Given:

(A)- If a pair of dice is thrown once, then the probability of getting a sum of 8 is 5/36.

(R)- In a simultaneous toss of two coins, the probability of getting exactly one head is 1/2.

Solution:

Take assertion,

Find the all possible condition for getting a sum of 8,

$\[ \Rightarrow \left( {5,3} \right),\left( {3,5} \right),\left( {4,4} \right),\left( {2,6} \right)\left( {6,2} \right)\]$

$\[n = 5\]$

Therefore the probability of getting a sum of 8 is,

$\[ = \frac{5}{{{6^2}}}\]$

$\[ = \frac{5}{{36}}\]$

Hence the assertion (A) is correct.

Take reason (R),

Write all possible outcomes,

$\[\left( {H,H} \right),\left( {H,T} \right),\left( {T,H} \right),\left( {T,T} \right)\]$

Therefore the probability of getting exactly one head is,

$\[ = \frac{2}{4}\]$

$\[ = \frac{1}{2}\]$

So that, reason (R) is also correct.

Hence, the correct answer is (b) i.e.  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).