Example 5-1. Probability Distribution for Tossing Three Coins.

Construct a probability distribution for a discrete random variable using a probability experiment of tossing three coins.

Toss three coins. The sample space is {TTT, TTH, THT, HTT, HHT, HTH, THH, HHH}.If X be the random variable of the number of heads, then X assumes values of 0, 1, 2, or 3.

Heads

No Heads

One Head

Two Heads

Three Heads

TTT

TTH, THT, HTT

HHT, HTH, THH

HHH

X

0

1

2

3

Probability

__/8

__/8__/8__/8

__/8__/8__/8

__/8

P(X)

__/8

__/8

__/8

__/8

X

P(X)

0

1

2

3

Example 5-2. Probability Distribution for Rolling a Single Die

Construct the probability distribution for rolling a single fair die.

The sample space for a single die is 1, 2, 3, 4, 5, 6, with each outcome having equal probability of 1/6.

X

P(X)

1

2

3

4

5

6

Example Based on Observation

Example 5-3. Number of World Series Games

The baseball World Series is played by the winner of the National League and the American League. The first team to win four games wins the World Series. In other words, the series will consist of four to seven games, depending on the individual victories.The data shown consist of 40 World Series events. The number of games played in each series is represented by the variable X.Find the probability P(X) for each X and construct a probability distribution.For the 40 World Series included, the winner was determined in four games 8 time, five games 7 times, six games 9 times, and seven games 16 times.

Solution:

X

P(X)

4

__/40 = ____

5

__/40 = ____

6

__/40 = ____

7

__/40 = ____