3 In a certain college, 55% of the students are women. Suppose we take a sample of two students. Use a probability tree to find the probability (a) that both chosen students are women. (b) that at least one of the two students is a woman.

a)

b) For this case we want the probability that  at least one of the two students is a woman.

At least mean that can be 1 one women or 2. Let X the number of women selected:

So then the final probability would be:

Step-by-step explanation:

For this case we have the situation described in the figure attached.

We define the following notation:

F= Select a random student women

M= Select a random student male

We have defined the prior probabilities:

We can define the sample space like this:

For this case we assume that the selection on each trial are independnet events.

Part a

We want to find this probability , using the indpendence condition we can do this:

Part b

For this case we want the probability that  at least one of the two students is a woman.

At least mean that can be 1 one women or 2. Let X the number of women selected:

So then the final probability would be:

i think the correct option is the second option.

the answer is  

a.

4,624π mm2

step-by-step explanation: