Question

A fair coin is tossed. If the result is a head, a pair of fair dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well shuffled pack of 11 cards numbered 2, 3, 4….., 12 is picked up and the number on the card is noted. The probability that the noted number is 7 or 8, is -

• A. 193/792
• B. 195/792
• C. 191/792
• D. None

Answer 1

Answer: (A)

193/792

Answer 2

Probability of getting a total of 7 or 8 on a pair of dice, is $\frac { 11 } { 36 }$ . P (head shows up and number 7 or 8 is noted) = $\frac { 1 } { 2 }$ × $\frac { 11 } { 36 }$ . Also, P (tail shows up and number 7 or 8 is noted)

= $\frac { 1 } { 2 }$ × $\frac { 2 } { 11 }$. Hence the required probability, = $\frac { 193 } { 792 }$ .