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Chapter 4: Q.4.73 (page 168)

Suppose in Problem 4.72 that the two teams are evenly matched and each has probability 1 2 of winning each game. Find the expected number of games played.

Short Answer

Expert verified

In the given information the answer isEX=5.8125

Step by step solution

01

Given Information

Given that the two players are evenly matched, evenly matched means the two teams are played same number of matches with equal probability.

The probability is12.

By the definition E(X)=∑xp(x).

Let E games played=EGP

Expected value isE(GP)=2∑xp(x).

02

Calculation

E[GP]=24×33124+512×C3412312+612×C33123122+712×C36123123

E[GP]=214+518+6532+7×532

=2×9332=5.8125

03

Step 3:Final Answer

The final answer isEX=5.8125

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