There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?
The probability that the selected council member is a woman is 3/5 or 0.6.
The total number of council members = 4 men + 6 women = 10 members.
When one council member is selected at random, the total number of possible outcomes is 10. The number of favorable outcomes (selecting a woman) is 6, as there are six women on the council.
Therefore, P(woman) = Number of favorable outcomes / Total number of possible outcomes = 6/10 = 3/5.
Explanation
This question is similar to Example 7 in the textbook context, where probability is calculated as favorable outcomes divided by total outcomes. The context shows P(girl) = 25/40 when selecting from 25 girls and 15 boys. Applying the same logic: with 6 women out of 10 total members, P(woman) = 6/10 = 3/5.
Solution Steps
Step 1: Calculate total number of council members = 4 men + 6 women = 10
Step 2: Identify total possible outcomes = 10 (any one member can be selected)
Step 3: Identify favorable outcomes = 6 (any one of the six women)
Step 4: Calculate probability = 6/10 = 3/5