Chapter 3: Q.3.3 (page 97)

Use Equation $(2.1)$ to compute in a hand of bridge the conditional probability that East has $3$ spades given that North and South have a combined total of $8$ spades.

Short Answer

Expert verified

The conditional probability is $0.339$

Step by step solution

Step 1:Given Information

The probability that East has $3$ spades given that North and South have a consolidated complete of $8$ spades is,

$P (East has 3 spades ∣ North-South has 8 spades) = \frac{P (East has 3, N - Shas 8)}{P (N - S has 8)}$

Step 2:Explanation

The probability that north and south has 8 spades is,

$P (N - S has 8) = \frac{(\begin{array}{l} 13 \\ 8 \end{array}) (\begin{array}{l} 39 \\ 18 \end{array})}{(\begin{array}{l} 52 \\ 26 \end{array})}$

$= 0.1618$

The probability that East has $3$ and North and South has $8$ spades is

$P (East has 3 and N-Shas 8) = \frac{(\begin{array}{l} 13 \\ 8 \end{array}) (\begin{array}{l} 39 \\ 18 \end{array}) (\begin{array}{l} 5 \\ 3 \end{array}) (\begin{array}{l} 21 \\ 10 \end{array})}{(\begin{array}{l} 52 \\ 26 \end{array}) (\begin{array}{l} 26 \\ 13 \end{array})}$

$= 0.0548$

Step 3:Final Answer

The conditional probability that East has $3$ spades and North and South have a combined total of $8$ spades,

$P (East has 3 spades ∣ North-South has 8 spades) = \frac{0.0548}{0.1618}$

$= 0.339$

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Use Equation $(2.1)$ to compute in a hand of bridge the conditional probability that East has $3$ spades given that North and South have a combined total of $8$ spades.

Short Answer

Step by step solution

Step 1:Given Information

Step 2:Explanation

Step 3:Final Answer

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Use Equation (2.1)to compute in a hand of bridge the conditional probability that East has 3spades given that North and South have a combined total of 8 spades.

Short Answer

Step by step solution

Step 1:Given Information

Step 2:Explanation

Step 3:Final Answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Discrete Mathematics

Statistics

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

Use Equation $(2.1)$ to compute in a hand of bridge the conditional probability that East has $3$ spades given that North and South have a combined total of $8$ spades.