Chapter 2: Q. 2.5 (page 51)

In a hand of bridge, find the probability that you have $5$ spades and your partner has the remaining $8$ .

Short Answer

Expert verified

$0.0000175 \dots$

The outcome space is all possible hands of the partner.

Step by step solution

Given Information.

Given that in the hand of the bridge.

Explanation.

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

$W h a t i s t h e p r o b a b i l i t y o f A = {y o u r p a r t n e r h a s 9 s p a d e s}$

The outcome space $S$ contains all the possible hands of my partner. Each of the $(\begin{array}{l} 39 \\ 13 \end{array})$ elements $S$ has an equal probability of happening (in a fair game).

Now if all of the $9$ spades have to be in the hand, the remaining $5$ cards can be chosen from the $30$ in $(\begin{matrix} 30 \\ 5 \end{matrix})$ ways. This is the number of hands in the event $A$ .

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

P (A) = \frac{| A |}{| S |} A \subseteq S, | X | - the number of elements of X

Finally:

$P (A) = \frac{(\begin{matrix} 30 \\ 5 \end{matrix})}{(\begin{array}{l} 39 \\ 13 \end{array})} = \frac{13}{740962} = 0.00001754475 \dots$

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In a hand of bridge, find the probability that you have $5$ spades and your partner has the remaining $8$ .

Short Answer

Step by step solution

Given Information.

Explanation.

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

Short Answer

Step by step solution

Given Information.

Explanation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Pure Maths

Statistics

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Decision Maths

Study anywhere. Anytime. Across all devices.

In a hand of bridge, find the probability that you have $5$ spades and your partner has the remaining $8$ .