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:

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~

won't that be plagrisim thought?

step-by-step explanation: