A family plans to have 3 children. For each birth, assume that the probability of a boy is the same as the probability of a girl. What is the probability that they will have at least one boy and at least one girl?
Question
A family plans to have 3 children. For each birth, assume that the probability of a boy is the same as the probability of a girl. What is the probability that they will have at least one boy and at least one girl?
Solution
To solve this problem, we can use the concept of probability.
Step 1: Calculate the total number of outcomes The total number of outcomes when a family has 3 children can be calculated as 2^3 = 8. This is because each child can be either a boy or a girl, and there are 3 children. So, the total outcomes are: BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG.
Step 2: Calculate the number of favorable outcomes The favorable outcomes are the ones where the family has at least one boy and one girl. So, we exclude the outcomes where all are boys (BBB) and all are girls (GGG). This leaves us with 6 favorable outcomes: BBG, BGB, BGG, GBB, GBG, GGB.
Step 3: Calculate the probability The probability of an event is calculated as the number of favorable outcomes divided by the total number of outcomes. So, the probability that the family will have at least one boy and one girl is 6/8 = 0.75 or 75%.
Similar Questions
Assuming that the chance of a baby being a boy or a girl is the same, calculate the following probabilities for a family with 3 children:a. Calculate the probability that a family with three children has: Question 1i. Pr(all males) =
A couple is planning to have three children. What is the probability that:a. All of the children will be girls?b. Two of the children will be boys?c. At least 2 of the children will be girls?d. The couple will have 2 boys at the most?
We now have all we need in order to find P(A).What is P(A), the probability of a family with three children having exactly two girls?
You have recently got married and you plan to have 4 children. If the probability that a child is a boy is 0.5, what is the probability that you will have exactly 3 boys?
Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl ?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.