A teach chooses a student at random from a class of 10 boys and 15 girls. Find the odds in favor of and the odds against each event.
Choosing a boy
favor of choosing a boy:
# of boys/# of total students, reduce
odds against choosing a boy:
# of girls/# of total students, reduce
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To find the odds in favor and the odds against choosing a boy, we first need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
The teacher is choosing one student from a class of 10 boys and 15 girls. Therefore, the total number of possible outcomes is the sum of the number of boys and girls, which is 10 + 15 = 25.
Number of Favorable Outcomes:
We want to find the number of favorable outcomes, which is the number of boys in the class. In this case, there are 10 boys.
Odds in Favor:
The odds in favor of an event are defined as the ratio of the number of favorable outcomes to the number of unfavorable outcomes. In this case, the odds in favor of choosing a boy can be calculated as:
Odds in Favor = Number of Favorable Outcomes / Number of Unfavorable Outcomes
Since there are no unfavorable outcomes (as we are selecting from the entire class), the odds in favor of choosing a boy are:
Odds in Favor = Number of Favorable Outcomes / 0 = 10 / 0
However, division by zero is undefined, which means that the odds in favor are undefined in this case.
Odds Against:
The odds against an event are defined as the ratio of the number of unfavorable outcomes to the number of favorable outcomes. In this case, the odds against choosing a boy can be calculated as:
Odds Against = Number of Unfavorable Outcomes / Number of Favorable Outcomes
Since there are no unfavorable outcomes (as we are selecting from the entire class), the odds against choosing a boy are:
Odds Against = Number of Unfavorable Outcomes / Number of Favorable Outcomes = 0 / 10 = 0
Therefore, the odds in favor of choosing a boy are undefined, and the odds against choosing a boy are 0.