A hat contains slips of paper with the names of boys and girls in a class. A name is randomly selected and returned to the hat. The slips of paper are mixed. Then another random selection is made.
Event A: The first selection is a boy.
Event B: The second selection is a girl.
What is the probability of both events happening?
To determine this, we need to know the ratio of boys to girls in the class. Let x be the number of boys and y be the number of girls. Then, the total number of students in the class is x + y.
The probability of Event A occurring is the ratio of boys to the total students in the class, which is given by x / (x + y).
Since the name selected in the first draw is returned to the hat, the probabilities remain the same for the second draw. The probability of Event B occurring is the ratio of girls to the total students in the class, which is given by y / (x + y).
To find the probability that both events occur, multiply the probabilities of the individual events: (x / (x + y)) * (y / (x + y)).