Question

Only 30% of the students in a certain liberal arts college are males.

Question 10 of 11

If two students from this college are selected at random, what is the probability that they are both males?

   0

   0.25

   0.51

   0.60

   0.09

Again, only 30% of the students in a certain liberal arts college are males.

If two students from this college are selected at random, what is the probability that they are of the same gender?

   0.21

   0.42

   0.49

   0.58

   0.09

Answer 1

Answer 10: 0.09

Here we have used binomial distribution to calculate probability.

P(Both are males) = 0.09

Answer 11: 0.58

Here, we have to calculate

P(Gender is same) = P(Both are males) + P(Both are females)

We already have P(Both Males) = 0.09.

Now, we need to find P(Both females)

Only 30% of the students in a certain liberal arts college are males. so 70% are females.

We will binomial distribution to calculate probability of females just like we did for males in answer 10.

P(Both females) = 0.49

P(Gender is same) = P(Both are males) + P(Both females) = 0.09 + 0.49 = 0.58