Question

A.The Murray family has produced 8 children.

Answer 1

Answer:

A. 0.2734 = 27.34% probability that there are an equal number of boys and girls

B. 0.2753 = 27.53% probability that she’ll answer exactly 5 questions correctly

Step-by-step explanation:

In each of these questions, the binomial probability distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

A.The Murray family has produced 8 children.

What is the probability that there are an equal number of boys and girls?

8 children means that $n = 8$

Each children is equally as likely to be a boy or a girl, which means that $p = 0.5$

This probability is P(X = 4). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 4) = C_{8,4}.(0.5)^{4}.(0.5)^{4} = 0.2734$

0.2734 = 27.34% probability that there are an equal number of boys and girls

B.Margie has the uncanny ability of being able to guess the correct answer to TRUE/FALSE questions with an 80% accuracy rate. Tomorrow’s test has 7 questions on it and she needs to answer 5 questions correctly in order to make the Honor Roll. If she guesses on every question, what is the probability that she’ll answer exactly 5 questions correctly?

80% accurracy rate means that $p = 0.8$

7 questions means that $n = 7$

The probability is P(X = 5). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{7,5}.(0.8)^{5}.(0.2)^{2} = 0.2753$

0.2753 = 27.53% probability that she’ll answer exactly 5 questions correctly