sasha has 5 red pens and 4 blue pens in her bag. she will randomly pick one pen, keep it, and then randomly pick a second pen. What is the probability that she will pick two blue pens

There are nine pens altogether, out of which 4 are blue.

So the probability of picking a blue the first time is P(B)=4/9.
Now that there are only 3 blue out of 8 left, so the probability of picking a second blue out of P(B)=8 is 3/8.
For both events to happen, we apply the multiplication rule to get
P(BB)=(4/9)*(3/8)

To find the probability that Sasha will pick two blue pens, we need to determine the total number of possible outcomes for picking two pens and the number of favorable outcomes where both pens are blue.

The total number of possible outcomes is the total number of ways Sasha can pick two pens from her bag, which can be calculated using the combination formula. In this case, she has 9 pens in total (5 red + 4 blue), and she wants to choose 2 pens. So the total number of possible outcomes is given by the combination function:

C(9, 2) = 9! / (2! * (9-2)!) = 9! / (2! * 7!) = (9 * 8) / (2 * 1) = 36.

Now, let's determine the number of favorable outcomes where both pens are blue. Since Sasha has 4 blue pens, she can choose 2 blue pens from these 4. The number of favorable outcomes is again given by the combination function:

C(4, 2) = 4! / (2! * (4-2)!) = 4! / (2! * 2!) = (4 * 3) / (2 * 1) = 6.

Therefore, the probability that Sasha will pick two blue pens is the number of favorable outcomes divided by the number of possible outcomes:

P(two blue pens) = favorable outcomes / possible outcomes = 6 / 36 = 1/6 = 0.1667.

So, the probability that Sasha will pick two blue pens is approximately 0.1667 or 16.67%.