Assume, as in Example 3 h, that 64 percent of twins are of the same sex. Given that a newborn se

Name: Problem 65, Chapter 3: A First Course in Probability
Uploaded: 2025-05-08T22:48:35-08:00
Duration: 2 min 23 s
Channel: Sheryl Ezze
Description: Assume, as in Example 3 h, that 64 percent of twins are of the same sex. Given that a newborn set of twins is of the same sex, what is the conditional probability that the twins are identical?

step 1 So we want to determine the probability that given that a woman is pregnant with two boys, that

Question

Assume, as in Example $3 \mathrm{h}$, that 64 percent of twins are of the same sex. Given that a newborn set of twins is of the same sex, what is the conditional probability that the twins are identical?

   Assume, as in Example $3 \mathrm{h}$, that 64 percent of twins are of the same sex. Given that a newborn set of twins is of the same sex, what is the conditional probability that the twins are identical?

A First Course in Probability

Sheldon Ross 9th Edition

Chapter 3, Problem 65

Instant Answer

Solved by Expert Sheryl Ezze

05/08/2025

Step 1

From Example 3h, we know that 64 percent of twins are of the same sex. Since identical twins are always of the same sex, we can assume that 64 percent of twins are identical. Show more…

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Assume, as in Example $3 \mathrm{h}$, that 64 percent of twins are of the same sex. Given that a newborn set of twins is of the same sex, what is the conditional probability that the twins are identical?

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Key Concepts

Conditional Probability

Conditional probability is the chance that an event occurs given that another event has already occurred. This concept allows us to update our estimates for the likelihood of an event based on additional information and is a fundamental component in many probability problems.

Bayes' Theorem

Bayes' Theorem provides a systematic way of updating initial beliefs or probabilities when new evidence is introduced. It essentially reverses conditional probabilities, enabling one to calculate the probability of a cause given an observed effect, which is instrumental in many real-world inference problems.

Law of Total Probability

The Law of Total Probability helps to compute the probability of an event by breaking it down into several mutually exclusive scenarios that cover the entire sample space. It is used to combine the probabilities of an event under different conditions, serving as a bridge between conditional and overall probabilities.

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