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 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 :

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 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) (13/36) (B) (19/36) (C) (19/72) (D) (15/72)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/51181c4a035b436d92f0f886f8264330-.png" /> P ( A )=(1/2) × (11/36)+(1/2) × (2/9)=(19/72)

$\frac{13}{36}$

$\frac{19}{36}$

$\frac{19}{72}$

$\frac{15}{72}$

$P (A) = \frac{1}{2} \times \frac{11}{36} + \frac{1}{2} \times \frac{2}{9} = \frac{19}{72}$

3613​

3619​

7219​

7215​

P(A)=21​×3611​+21​×92​=7219​

$\frac{13}{36}$

$\frac{19}{36}$

$\frac{19}{72}$

$\frac{15}{72}$

$P (A) = \frac{1}{2} \times \frac{11}{36} + \frac{1}{2} \times \frac{2}{9} = \frac{19}{72}$