at a track meet with 135 participants, 25 participate in jumping event, 1/5 of these jumpers are female, and 1/3 of the the total participants are female. What is the probability that a participant chosen at random is a jumper, given that the person is a female? Please help?

To find the probability that a participant chosen at random is a jumper, given that the person is a female, we need to use conditional probability.

Let's break down the information given:

- There are 135 participants in total.
- 1/3 of the total participants are female.
- 25 participants are jumpers.
- 1/5 of the jumpers are female.

First, let's find the number of female participants. We know that 1/3 of the total participants are female, so we can calculate:

Female participants = (1/3) * 135

Next, let's find the number of female jumpers. We know that 1/5 of the jumpers are female, so we can calculate:

Female jumpers = (1/5) * 25

Now, we can find the probability that a participant chosen at random is a female jumper. This is calculated by dividing the number of female jumpers by the number of female participants:

Probability = Female jumpers / Female participants

Now let's plug the numbers into the formula:

Probability = (1/5) * 25 / ((1/3) * 135)

Simplifying the expression:

Probability = 5/5 * 25 / 1/3 * 135

Probability = 25 / (1/3 * 135)

Probability = 25 / (135/3)

Probability = 25 * (3/135)

Probability = 75 / 135

Finally, we simplify the fraction and convert it into decimal form:

Probability ≈ 0.556

So, the probability that a participant chosen at random is a jumper, given that the person is a female, is approximately 0.556, or 55.6%.