Chapter 5.2, Problem 32E

(a)

To determine

To find: Probability distribution of chance process

Answer to Problem 32E

  $P(S=s)=\frac{1}{8}\text{ for s = }$ (H,H,H), (H,H,T), (H,T,T), (H,T,H), (T,H,H), (T,H,T), (T,T,T), (T,T,H)

Explanation of Solution

Given:

A fair coin is tossed 3 times.

Calculation:

Sample space : (H,H,H), (H,H,T), (H,T,T), (H,T,H), (T,H,H), (T,H,T), (T,T,T), (T,T,H)

Total number of outcomes $=8$

Since, each outcome has an equal chance of coming, so each outcome will have probability equal to $\frac{1}{8}$ .

(b)

To determine

To find: Probability of event B.

Answer to Problem 32E

The probability of getting more heads than tails is 0.5.

Explanation of Solution

Given information:

Event B is the event of getting more heads than tails.

This means − 0 tails, 3 heads

1 tail, 2 heads

Formula used:

Probability of getting more heads than tails = $\frac{\text{Number of outcomes with heads more than tails}}{\text{Total number of outcomes}}$

Calculation:

Probability of event B

Total number of outcomes with 0 tail and 3 heads $=1$

Total number of outcomes with 1 tail and 2 heads $=3$

The required probability = $\frac{1+3}{8}=0.5$