Questions: The sample space listing the eight simple events that are possible when a couple has three children is bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg. After identifying the sample space for a couple having four children, find the probability of getting four girls and no boys. Identify the sample space for a couple having four children.

The sample space listing the eight simple events that are possible when a couple has three children is bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg. After identifying the sample space for a couple having four children, find the probability of getting four girls and no boys. Identify the sample space for a couple having four children.
Transcript text: The sample space listing the eight simple events that are possible when a couple has three children is $\{b b b, b b g, b g b, b g g, g b b, gbg, ggb, ggg\}$. After identifying the sample space for a couple having four children, find the probability of getting four girls and no boys. Identify the sample space for a couple having four children. $\square$
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the Sample Space for \(n\) Children

The total number of possible outcomes for \(n=4\) children is \(2^4 = 16\).

Step 2: Calculate the Number of Favorable Outcomes

The number of ways to have \(k=4\) children of a specific gender out of \(n=4\) is given by \(\binom{n}{k} = \frac{n!}{k!(n-k)!} = 1\).

Step 3: Calculate the Probability

The probability of having \(k=4\) children of a specific gender out of \(n=4\) is \(\frac{\binom{n}{k}}{2^n} = 0.06\).

Final Answer:

The probability of having \(k=4\) children of a specific gender when a couple has \(n=4\) children is approximately 0.06.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Estimating a Population Question 3, 9.2.17 A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x̄, is found to be 106, and the sample standard deviation, s, is found to be 10. (a) Construct an 80% confidence interval about μ it the sample size, n, is 18. (b) Construct an 80% confidence interval about μ if the sample size, n, is 26. (c) Construct a 90% confidence interval about μ if the sample size, n, is 18. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? (b) Construct an 80% confidence interval about μ if the sample size, n, is 26. Lower bound: 103.4; Upper bound: 108.6 How does increasing the sample size affect the margin of error, E? A. As the sample size increases, the margin of error increases. B. As the sample size increases, the margin of error decreases. C. As the sample size increases, the margin of error stays the same. (c) Construct a 90% confidence interval about μ if the sample size, n, is 18. Lower bound: 101.9; Upper bound: 110.1 Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? A. As the level of confidence increases, the size of the interval increases. B. As the level of confidence increases, the size of the interval decreases. C. As the level of confidence increases, the size of the interval stays the same.
failedAnswered
Identify the species that is oxidized and the species that is reduced in each reaction. Write out two half reactions to show how many electrons are gained or lost by each species. a. Mg + Fe^2+ -> Mg^2+ + Fe b. Cu^2+ + Sn -> Sn^2+ + Cu c. 4 Na + O2 -> 2 Na2 O
failedAnswered
Question 6 of 12, Step 1 of 2 The number of assaults in a city is depicted in two different graphs below. Assault Counts Graph A Assault Counts Graph B Step 1 of 2: How many times as many assaults were there actually in Year 3 compared to Year 1? Round your answer to 2 decimal places.
failedAnswered
2. What is the density of a 7.485 gram piece of metal that causes the level of water in a graduated cylinder to rise from 5.2 to 6.8 mL when the metal is submerged in the water? Consider significant figures when doing the calculation.
failedAnswered
For each expression, select all equivalent expressions from the list. (a) x+x+x: O x+3, O 3x, O 2x-x, O 3+x (b) 24y-16: O 8(3y-2), O 8y, O 12y-8, O 8 · 3y-8 · 2