Question

A coin is tossed and a die is rolled one after the other. What is the probability of flipping a tail and seeing a 4 or flipping a head and seeing a 6?

• A. $\frac{1}{2}$
• B. $\frac{1}{12}$
• C. $\frac{1}{6}$
• D. $\frac{1}{24}$

Answer 1

The correct option is C $\frac{1}{6}$

$\underset{–}{ConceptInvolved:}$

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

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

$\underset{–}{Method:}$

P((tail and 4) or (head and 6)) = P(tail and 4) + P(head and 6)

Case 1:
P(tail and 4) = P(tail) $\times$ P(4)

P(tail and 4) $=\frac{1}{2}\times \frac{1}{6}=\frac{1}{12}$

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

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

P((tail and 4) or (head and 6)) $=\frac{1}{12}+\frac{1}{12}$

P((tail and 4) or (head and 6)) $=\frac{1}{6}$