Question

A math class consists of 21 female students and 16 male students. Two students are selected at random to participate in a probability experiment. Compute the following probabilities. Write your answers in decimal form. Round to the nearest thousandth as needed.a. A male is selected, then a female. b. A female is selected, then a male. c. Two males are selected. d. Two females are selected. e. No males are selected.

Answer 1

In a math class with 21 female students and 16 male students, we can calculate the probabilities of various scenarios when two students are randomly selected. The probabilities are as follows: a. Male then female: 0.246, b. Female then male: 0.242, c. Two males: 0.222, d. Two females: 0.315, e. No males: 0.315.

Step-by-step explanation:

To compute the probabilities, we need to determine the total number of students and the number of males and females separately. There are a total of 37 students in the math class (21 females + 16 males).

a. To calculate the probability of selecting a male and then a female, we multiply the probability of selecting a male (16/37) by the probability of selecting a female from the remaining students (21/36). This gives us (16/37) * (21/36) = 0.246.

b. To calculate the probability of selecting a female and then a male, we multiply the probability of selecting a female (21/37) by the probability of selecting a male from the remaining students (16/36). This gives us (21/37) * (16/36) = 0.242.

c. To calculate the probability of selecting two males, we multiply the probability of selecting a male (16/37) by the probability of selecting another male from the remaining students (15/36). This gives us (16/37) * (15/36) = 0.222.

d. To calculate the probability of selecting two females, we multiply the probability of selecting a female (21/37) by the probability of selecting another female from the remaining students (20/36). This gives us (21/37) * (20/36) = 0.315.

e. To calculate the probability of not selecting any males, we need to calculate the probability of selecting two females. This was calculated in part d as 0.315.