Question

At your​ school, 20​% of the class are marketing majors. You are randomly assigned to two partners in your statistics class. ​a) What is the probability that the first partner will be a marketing​ major? ​b) What is the probability that the first partner​ won't be a marketing​ major? ​c) What is the probability that both will be marketing​ majors? ​d) What is the probability that at least one will be a marketing​ major?

Answer 1

Answer:

a) 20%

b) 80%

c) There is 4% probability that both will be marketing majors.

d) There is a 36% probability that at least one will be a marketing​ major.

Step-by-step explanation:

At your​ school, 20​% of the class are marketing majors.

This means that for each student, there is a 20% that he is a marketing major and an 80% chance that he is not a marketing major.

a) What is the probability that the first partner will be a marketing​ major?

The probabilities for each student are independent, so it is 20%.

​b) What is the probability that the first partner​ won't be a marketing​ major?

80%

c) What is the probability that both will be marketing​ majors?

For each one, it is 20%. So:

$P = 0.2*0.2 = 0.04$

There is 4% probability that both will be marketing majors.

​d) What is the probability that at least one will be a marketing​ major?

That is one of them or both. For both, we found in c) that it is 4%.

For one of them, there are two cases. Either the first partner is and the second is not, or the other way. So, the probability that at least one will be a marketing major is

$P = 0.04 + 2*0.2*0.8 = 0.36$

There is a 36% probability that at least one will be a marketing​ major.