Question

A fair coin is tossed if the result is a head, a pairof fair dice is rolled and the score is noted. If theresult is a tail, a card from a well shuffled pack ofeleven numbered 1,2,3,.......11 is picked and thenumber on the card is noted. Then the probabilitythat the number noted is either 7 or 8 is

• A. $\frac{45}{512}$
• B. $\frac{193}{792}$
• C. $\frac{193}{1024}$
• D. $\frac{243}{792}$

Answer 1

The correct option is B $\frac{193}{792}$

P(7 or 8)= P(7or8/head).P(head)+P(7or8/tail)P(tail)
P(7or8/head)= P(sum of dice=7)+P(sum of dice=8) = $5/36+6/36=11/36$
P(7or8/tail)= $2/11$
Therefore P(7 or 8)= $\frac{11}{36}\times \frac{1}{2}+\frac{2}{11}\times \frac{1}{2}=\frac{193}{792}$