Question

A die is rolled and a coin is tossed one after the other. What is the probability of rolling 1 and flipping a head or rolling 6 and flipping a tail?

Answer 1

Concept involved:

P(A or B) = P(A) $+$ P(B)

P(A and B) = P(A) $\times$ P(B)

P((Head and 1) or (Tail and 6)) = P(Head and 1) + P(Tail and 6)

Case 1:
P(Head and 1) = P(Head) $\times$ P(1)

P(Head and 1) $=\frac{1}{2}\times \frac{1}{6}=\frac{1}{12}$

Case 2:
P(Tail and 6) = P(Tail) $\times$ P(6)

P(Tail and 6) $=\frac{1}{2}\times \frac{1}{6}=\frac{1}{12}$

P((Head and 1) or (Tail and 6)) $=\frac{1}{12}+\frac{1}{12}$

P((Head and 1) or (Tail and 6)) $=\frac{1}{6}$