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.
Let's break down the information given:
- The total number of members in the health club is 500.
- 30% of the members are joggers, which means the number of joggers is (30/100) * 500 = 150.
- 55% of the joggers are female, so the number of female joggers is (55/100) * 150 = 82.5.
However, we can't have a fraction of a person, so we need to round this number. Since we're dealing with people, it makes sense to round to the nearest whole number.
Rounding 82.5 to the nearest whole number gives us 83 female joggers.
- Therefore, the number of male joggers is 150 - 83 = 67.
Now, we can divide the number of male joggers by the total number of members in the health club:
Probability of a member being a male jogger = (Number of male joggers / Total number of members) = 67 / 500 ≈ 0.134.
Therefore, the probability that a member is a male jogger is approximately 0.134 or 13.4%.