Question

An unbiased coin is tossed. If the result is a head, a pair of unbiased 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 eleven cards numbered 2, 3, 4, ……, 12 is picked and the number on the card is noted. The probability that the noted number is either 7 or 8, is

• A. 0.24
• B. 0.244
• C. 0.024
• D. None of these

Answer 1

The correct option is B 0.244

Required probability = probability that either the number is 7 or the number is 8.
i.e., Required Probability $=P_7+P_8$
Now $P_7=\frac{1}{2}.\frac{1}{11}+\frac{1}{2}.\frac{6}{36}=\frac{1}{2}(\frac{1}{11}+\frac{1}{6})$
$P_8=\frac{1}{2}.\frac{1}{11}+\frac{1}{2}.\frac{5}{36}=\frac{1}{2}(\frac{1}{11}+\frac{5}{36})$
$\therefore P=\frac{1}{2}(\frac{2}{11}+\frac{11}{36})=0.244$