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Chapter 2: Q. 2.5 (page 51)

In a hand of bridge, find the probability that you have5spades and your partner has the remaining8.

Short Answer

Expert verified

0.0000175鈥�

The outcome space is all possible hands of the partner.

Step by step solution

01

Given Information.

Given that in the hand of the bridge.

02

Explanation.

Experiment: A fair game of bridge. You have 5spades.

WhatistheprobabilityofA={yourpartnerhas9spades}

The outcome space Scontains all the possible hands of my partner. Each of the 3913elements Shas an equal probability of happening (in a fair game).

Now if all of the 9spades have to be in the hand, the remaining5cards can be chosen from the30in 305ways. This is the number of hands in the eventA.

The Axioms of probability for a sample space of equally likely events derive the formula:

P(A)=|A||S|A鈯�S,|X|-the number of elements ofX

Finally:

P(A)=3053913=13740962=0.00001754475鈥�

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