3. A couple is planning on having four children. Assume that the probabilities of the man fathering a boy or a girl are .50 and .50, respectively. What is the probability that
a. exactly two will be boys,
b. fewer than two will be boys, and
c. more than one will be a boy?
Answer
c. more than one will be a boy
4. You draw three cards (with replacement) from a standard deck of cards. What is the probability that
a. exactly one will be red,
b. none will be red, and
c. more than two will be red?
Answer
b. none will be red
14. Assume a man has a .50 chance of fathering a boy and a .50 chance of fathering a girl. He father three children. What is the probability that
a. all three will be girls,
b. exactly two will be girls, and
c. at least two will be girls?
Answer
c. At least two will be girls
You are not answering the questions that are being asked. They are asking for probabilities.
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though. However, here is a start.
Rewording the questions can be helpful.
3b. Only one will be a boy.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
3c. 2, 3, or 4 boys.
Either-or probabilities are found by adding the individual probabilities.
4b. All would be black.
4c. 3 or 4 would be red, or 1 or 2 would be black.
14. 2, 3, or 4 girls.
A couple intends to have 4 children. Assume that having a boy and having a girl are equally likely events. Find the probability that the couple has two boys and two girls.
50
25
To find the probability in each scenario, we need to use the concept of probability and the multiplication rule.
a. To find the probability that exactly two will be boys:
Since the probability of having a boy or girl is 0.50 each, we can use the binomial probability formula. The formula is: P(x) = C(n,x) * p^x * q^(n-x)
Here, n is the total number of children, x is the number of boys, p is the probability of a boy (0.50), and q is the probability of a girl (1 - p = 0.50).
So, the probability of exactly two boys in a family of four children is: P(2 boys) = C(4, 2) * 0.50^2 * 0.50^(4-2)
b. To find the probability that fewer than two will be boys:
We can sum the probabilities of having one boy and no boys.
P(fewer than two boys) = P(1 boy) + P(no boys)
c. To find the probability that more than one will be a boy:
We can sum the probabilities of having two boys, three boys, and four boys.
P(more than one boy) = P(2 boys) + P(3 boys) + P(4 boys)
For questions 4 and 14, you can follow the same approach using the respective probabilities given.
Please note that the probabilities calculated using this method assume that the events (having a boy or girl, drawing cards) are independent and each child or card draw has the same probability of occurrence.