Question

A coin is tossed and a square spinner labeled A,B, C,D is twirled. Determine the probability of obtaining: a tail or a vowel ( or both)

Answer 1

To determine the probability of obtaining a tail or a vowel ( or both

$\begin{gathered} \text{ For Coin HT } \\ \text{Prob( a tail) = }\frac{1}{2} \\ \text{For Vowel ABCD} \\ \text{Prob( a vowel) = }\frac{1}{4} \end{gathered}$$\begin{gathered} P(\text{T}\cup\text{V) = P(T) + P(V) - P(T}\cap\text{V}) \\ P(T\cup V)\text{ = }\frac{1}{2}+\frac{1}{4}\text{ - }\frac{1}{2}.\frac{1}{4}\text{ = }\frac{1}{2}+\frac{1}{4}-\frac{1}{8} \\ P(T\cup V)\text{ = }\frac{4+2-1}{8} \\ P(T\cup V)\text{ = }\frac{5}{8} \\ \end{gathered}$

Hence the probability of obtaining a tail or a vowel ( or both) = 5/8