A new shoe comes in two colors, black or red, and in sizes from 5 to 12, including half sizes. If a pair of the shoes chosen at random for a store display, what is the probability it will be red and size 9 or larger?
So it could be sizes: 9, 9.5, 10, 10.5, 11, 11.5 or 12
let's pick one of the sizes, say size 10
prob (red, and size 10) = (1/2)(1/14) , (there are 14 possible sizes)
but the same probability is true for any of the 7 required sizes
prob(your event) = 7(1/2)(1/14) = 1/4
To find the probability, we need to determine the total number of possible outcomes and the number of successful outcomes.
1. Determine the total number of possible outcomes:
Since the shoe comes in two colors (black or red) and sizes from 5 to 12 (including half sizes), we have a total of:
- Colors: 2 (black or red)
- Sizes: 8 (5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5)
Therefore, the total number of possible outcomes is 2 (colors) * 8 (sizes) = 16.
2. Determine the number of successful outcomes:
We need to find the number of shoes that are red and size 9 or larger:
- Colors: 1 (red)
- Sizes: 4 (9, 9.5, 10, 10.5)
Therefore, the number of successful outcomes is 1 (color) * 4 (sizes) = 4.
3. Calculate the probability:
The probability of an outcome occurring is given by the ratio of the number of successful outcomes to the total number of possible outcomes.
Probability = Number of successful outcomes / Total number of possible outcomes
= 4 (successful outcomes) / 16 (possible outcomes)
= 1/4
= 0.25
= 25%
Therefore, the probability that a randomly chosen shoe for the store display will be red and size 9 or larger is 25%.