A couple is planning to have 3 children. Assuming that having a boy and having a girl are equally likely, and that the gender of one child has no influence on (or, is independent of) the gender of another, what is the probability that the couple will have exactly 2 girls?The "random experiment" in this case is having 3 children, as odd as that may sound in this context. The next and most important step is to determine what all of the possible outcomes are, and list them (i.e., list the sample space S). In this case, each outcome represents a possible combination of genders of 3 children (note that examples with the same number of boys and girls but a different birth order must be listed separately).What is the sample space in this case? (Use B for boy and G for girl).

Recall the couple that is planning to have 3 children, where the sample space S of all possible outcomes is:S={BBB, BBG, BGB, GBB, GGB, GBG, BGG, GGG}Consider the following two events:A—the middle child is a girlC—the three children are of the same genderIn the box below, answer the following:i. What are the possible outcomes for each of these events?ii. Do the events share any of the outcomes? (i.e., is there an overlap between the two events?)iii. Based on ii, are the events disjoint or not?

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?

A couple decides to have three children. Let A define the event that the couple has at least 1 girl. What are the possible outcomes for this event? (G=girl, B=boy) {G, BG, BBG} {G, GG, GGG} {BBB, BBG, BGB, GBB, GGB, GBG, BGG, GGG} {GGG, GGB, GBG, BGG, GBB, BGB, BBG} {GBB, BGB, BBG}

To determine the probability of a couple having two children and both are girls, you:Group of answer choicesmultiply the probabilities of each event happening separately (i.e., ½ x ½ = ¼).add their individual probabilities (i.e., ½ + ½ = 1).

Since both genders are equally likely, and since the gender of one child does not affect the gender of another, in this scenario all 8 outcomes are equally likely (each having probability 1/8).Now we're getting to our event of interest: "Having exactly two girls." Let's denote this event by A.How many of the 8 outcomes satisfy (or make up) event A? List them.