Question

A coin is tossed, then a letter from the word INDIANAPOLIS is selected at random. Find each probability. P( heads, then P) P( tails, then a vowel) P( tails, then N) P( heads, then D or I)

Answer 1

$Pr(Head)=\dfrac{1}{2}=P(Tail)$

There are 12 letters in the word INDIANAPOLIS: 6 vowels and 6 consonants.

$$Pr(P)=\dfrac{1}{12}$$

$$Pr(Vowel)=\dfrac{6}{12}=\dfrac{1}{2}$$

$$Pr(N)=\dfrac{2}{12}=\dfrac{1}{6}$$

$$Pr(D\cup I)=\dfrac{4}{12}=\dfrac{1}{3}$$

Then

$$Pr(Head, P)=\dfrac{1}{2}\cdot \dfrac{1}{12}=\dfrac{1}{24}$$

$$Pr(Tail, Vowel)=\dfrac{1}{2}\cdot \dfrac{1}{2}=\dfrac{1}{4}$$

$$Pr(Tail, N)=\dfrac{1}{2}\cdot \dfrac{1}{6}=\dfrac{1}{12}$$

$$Pr(Head, D\cup I)=\dfrac{1}{2}\cdot \dfrac{1}{3}=\dfrac{1}{6}$$