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%.