At a track meet with 190 participants, 20 participate in jumping events, 1/4 of these jumpers are female, and 1/2 of 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?
20 jump
1/4 of those = 5 are female jumpers
1/2 of 190 = 95 are female
So, p(jumper|female) = 5/95
To calculate the probability that a participant chosen at random is a jumper, given that the person is a female, we need to find the number of female jumpers and divide it by the total number of females at the track meet.
1. Find the number of female jumpers:
- Given that 1/4 of the jumpers are female and there are 20 jumpers in total, we have 1/4 * 20 = 5 female jumpers.
2. Find the total number of females at the track meet:
- Given that 1/2 of the total participants are female, we have 1/2 * 190 = 95 females.
3. Calculate the probability:
- The probability that a participant chosen at random is a jumper, given that the person is a female, is the number of female jumpers divided by the total number of females.
- Probability = Number of female jumpers / Total number of females = 5 / 95 = 1/19.
Therefore, the probability that a participant chosen at random is a jumper, given that the person is a female, is 1/19.
To find the probability that a participant chosen at random is a jumper, given that the person is a female, we first need to determine the number of female jumpers and the number of total females.
Given that 1/4 of the jumpers are female, we can calculate the number of female jumpers by multiplying the total number of jumpers by 1/4.
Number of female jumpers = (1/4) * 20 = 5
Given that 1/2 of the total participants are female, we can calculate the number of total females by multiplying the total number of participants by 1/2.
Number of females = (1/2) * 190 = 95
Now, we can find the probability by dividing the number of female jumpers by the number of females.
Probability = Number of female jumpers / Number of females = 5 / 95
Therefore, the probability that a participant chosen at random is a jumper, given that the person is a female, is 5/95, which can be simplified to 1/19.