Question

An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in a tail then a card from a well-shuffled pack of nine cards numbered $1,2,3,..,9$ is randomly picked and the number on the card is noted. The probability that the noted number is either $7$ or $8$ is?

• A. $\frac{13}{36}$
• B. $\frac{19}{36}$
• C. $\frac{19}{72}$
• D. $\frac{15}{72}$

Answer 1

The correct option is C $\frac{19}{72}$

$P\left(7or8\right)$

$=P\left(H\right)P\left(7or8\right)+P\left(T\right)P\left(7or8\right)$(head then sum on dice 7 or 8,tell then number on ticket 7 or 8)

$=\frac{1}{2}\times \frac{11}{36}+\frac{1}{2}\times \frac{2}{9}=\frac{19}{72}$.