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 solve this problem, we need to find the probability that a randomly chosen participant is a jumper, given that the person is a female. We can break down the steps as follows:
Step 1: Calculate the number of female participants at the track meet.
Given that 1/3 of the total participants are female, we can multiply the total number of participants (135) by 1/3 to find the number of female participants:
Number of female participants = 135 * (1/3) = 45
Step 2: Calculate the number of female jumpers.
Given that 1/5 of the jumpers are female, we can multiply the number of jumpers (25) by 1/5 to find the number of female jumpers:
Number of female jumpers = 25 * (1/5) = 5
Step 3: Calculate the probability.
The probability of a participant being a jumper, given that they are female, is the number of female jumpers divided by the number of female participants:
Probability = Number of female jumpers / Number of female participants
Probability = 5 / 45 = 1/9
Therefore, the probability that a participant chosen at random is a jumper, given that the person is a female, is 1/9.