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 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}

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).

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).

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?

Assume that it is equally likely for a child to be born a boy or a girl, and that the Lin family is planning on having three children.List the elements of the event that the Lins have at least one girl. (Use B to represent boy, and G to represent girl. For example, if there are three girls born, it would be represented as GGG. Enter your answers as a comma-separated list.){