Question

Question 24 (ii)
A die is thrown twice. What is the probability that 5 will come up at least once?

Answer 1

Let S be the sample space associated with the random experiment of throwing a die twice.
Then, n(S) = 36
$\therefore$ A B= first and second throw show 5, i.e., getting 5 in each throw.
We have, A = (5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
And B = (1,5)(2,5)(3,5)(4,5)(5,5)(6,5)
$\therefore$ P(A) = P(B) = $\frac{6}{36}$ and P(A $\cap$ B) = $\frac{1}{36}$
$\therefore$ Required probability= Probability that at least one of the two throws shows 5.
= P(A$\cup$B) = P(A) + P(B) - P(A$\cap$B)
= $\frac{6}{36}+\frac{6}{36}-\frac{1}{36}=\frac{11}{36}$