30 percent of the members of a health club are joggers. 55 percent of the joggers are female, and 60 percent of the non-joggers are female. If 500 people are members of the health club, what is the probability that a member is a male jogger? Explain.
To find the probability that a member is a male jogger, we need to calculate the number of male joggers and divide it by the total number of members in the health club.
Given information:
1. 30 percent of the members of the health club are joggers.
2. 55 percent of the joggers are female.
3. 60 percent of the non-joggers are female.
4. There are 500 people who are members of the health club.
Let's break down the calculations step by step:
Step 1: Calculate the number of joggers in the health club.
Since 30 percent of the members are joggers and there are 500 members, we can calculate the number of joggers as follows:
Number of joggers = (30/100) * 500 = 0.3 * 500 = 150 joggers.
Step 2: Calculate the number of female joggers.
Since 55 percent of the joggers are female, we can calculate the number of female joggers as follows:
Number of female joggers = (55/100) * 150 = 0.55 * 150 = 82.5.
Step 3: Calculate the number of non-joggers.
The total number of members in the health club is 500, and we know that 30 percent are joggers. So the number of non-joggers can be calculated as follows:
Number of non-joggers = 500 - 150 (the number of joggers) = 350 non-joggers.
Step 4: Calculate the number of female non-joggers.
Since 60 percent of the non-joggers are female, we can calculate the number of female non-joggers as follows:
Number of female non-joggers = (60/100) * 350 = 0.6 * 350 = 210.
Step 5: Calculate the number of male joggers.
To find the number of male joggers, we need to subtract the number of female joggers from the total number of joggers:
Number of male joggers = Total number of joggers - Number of female joggers = 150 - 82.5 = 67.5.
Step 6: Calculate the probability of a member being a male jogger.
Finally, we calculate the probability that a member is a male jogger by dividing the number of male joggers by the total number of members:
Probability = Number of male joggers / Total number of members = 67.5 / 500 = 0.135.
Therefore, the probability that a member is a male jogger is 0.135, or 13.5%.