A unbiased coin is tossed. If the result is a head a pair of unbiased dice is rolled and the sum of the numbers obtained is noted. If the result is a tail, card from a well shuffled pack of eleven cards numbered 2, 3, 4, ………12 is picked and the number on the card is noted. What is the probability that the noted number is either 7 or 8?

Explanation

`E_{1}=` coin represents a head


`E_{2}=` coin represents a head


`A=` noted number is 7 or 8


`therefore P(E_{1})=frac{1}{2}`


`P(E_{2})=frac{1}{2}`


`P(A / E_{1})=frac{11}{36} `


`P(A / E_{2})=frac{2}{11}
`


...