Question

a math class consists of 21 female students and 22 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. 0.280 incorrect 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

To compute the probabilities, we need to determine the total number of students and the total number of ways in which we can select two students. We can then calculate the probabilities based on the given information.

Step-by-step explanation:

To compute the probabilities, we need to determine the total number of students and the total number of ways in which we can select two students. There are 21 female students and 22 male students, so the total number of students is 43. Now, let's calculate the probabilities.

a. To calculate the probability of selecting a male, and then a female, we multiply the probabilities of each event. The probability of selecting a male is 22/43, and the probability of selecting a female after selecting a male is 21/42 (since there is one less female available). So the probability is (22/43) * (21/42) = 0.273.

b. To calculate the probability of selecting a female, and then a male, we follow the same logic. The probability of selecting a female is 21/43, and the probability of selecting a male after selecting a female is 22/42. So the probability is (21/43) * (22/42) = 0.252.

c. To calculate the probability of selecting two males, we multiply the probability of selecting the first male (22/43) by the probability of selecting the second male (21/42). So the probability is (22/43) * (21/42) = 0.273.

d. To calculate the probability of selecting two females, we follow the same logic. The probability of selecting the first female is 21/43, and the probability of selecting the second female is 20/42. So the probability is (21/43) * (20/42) = 0.252.

e. To calculate the probability of not selecting any males, we need to calculate the probability of selecting two females. We already know that the probability of selecting a female as the first student is 21/43. Since there is one less male available after the first selection, the probability of selecting a female as the second student is 20/42. So the probability is (21/43) * (20/42) = 0.234.