Question

Assertion: In a cricket match, a batsman hits 9 boundaries out of 45 balls he plays. The probability that in a given throw he does not hit the boundary is $\frac{4}{5}$.
Reason: $P\left(E\right)+P(\mathrm{not}E)=1$.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Answer 1

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.

Explanation:
Total number of balls = 45
Number of times the ball hits the boundary = 9
Number of times the ball does not hit the boundary = (45 − 9 ) = 36

Let E be the event that the ball hits the boundary.Then,

P(E) = $\frac{9}{45}=\frac{1}{5}$

P(not E) = P( he does not hit the boundary) = $\left(1-\frac{1}{5}\right)=\frac{4}{5}$ [ P(not E)​ = $\frac{36}{45}=\frac{4}{5}$]
Also, P(E) + P(not E) ​ = 1 is true.

Thus, Assertion ( A) and Reason (R) are true and Reason ( R) is a correct explanation of Assertion (A).
So, the correct answer is (a).