Question: Compute the odds in favor of obtaining at least 1 head when a single coin is tossed 2 times. The…

Compute the odds in favor of obtaining at least 1 head when a single coin is tossed 2 times.

The odds in favor are . (Type a fraction.)

Solution

To find the odds in favor of obtaining at least 1 head when a single coin is tossed 2 times, we can follow these steps: First, determine the total possible outcomes when a coin is tossed twice. The possible outcomes are: - HH (Head, Head) - HT (Head, Tail) - TH (Tail, Head) - TT (Tail, Tail) So, there are 4 possible outcomes. Next, calculate the number of favorable outcomes for obtaining at least 1 head. These outcomes are: - HH - HT - TH Thus, there are 3 favorable outcomes. Now, calculate the number of unfavorable outcomes (where no heads are obtained): - TT There is 1 unfavorable outcome. The odds in favor of an event are given by the ratio of the number of favorable outcomes to the number of unfavorable outcomes. Therefore, the odds in favor of obtaining at least 1 head are: \[ \frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}} = \frac{3}{1} \] So, the odds in favor are \( \frac{3}{1} \).