   Chapter 9.2, Problem 13ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# A coin is tossed four times. Each time the result H (or heads or T for tails is recorded. An outcome of HHTT means that heads were obtained on the first two tosses and tails on the second two. Assume that heads and tails are equally likely on each toss. a. How many distinct outcomes are possible? b. What is the probability that exactly two heads occur? c. What is the probability that exactly one head occurs?

To determine

(a)

Total possible disticnt outcomes.

Explanation

Given information:

A coin is tossed tour times. Each time the result H for heads or T for tails is recorded. An outcome of HHTT means that heads were obtained on the first two tosses and tails on the second two. Assume that heads and tails are equally likely on each toss.

Concept used:

T: Tail of coin

Head and tails are equally likely.

Calculation:

When a coin is tossed, the outcomes are either heads or a tails.

When a coin is tossed 4 times, the total possible outcomes are 2×2×2×2=16 by the rule of multiplication.

S={HHHH,HHHT,HTHH,T

To determine

(b)

The probability of getting exactly two heads occur.

To determine

(c)

The probability that exactly one head occurs.

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