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 is chosen at random for a store display, what is the probability it will be red and size 9 or larger?
This was horrible they didn’t even give the answer wtf
To calculate the probability, we need to determine the total number of possible shoe combinations and the number of favorable outcomes.
First, let's calculate the total number of possible shoe combinations. We have two color options (black or red) and sizes ranging from 5 to 12, including half sizes. Therefore, there are 2 color options and (12 - 5 + 1) = 8 size options. Thus, the total number of possible shoe combinations is 2 × 8 = 16.
Next, let's determine the number of favorable outcomes, which means finding the number of red shoes with a size of 9 or larger.
Since we have two color options (black or red), we can assume that half the shoes are red. Thus, the number of red shoes would be half the total number of shoe combinations, which is 16 / 2 = 8.
Since we're interested in shoes with a size of 9 or larger, we need to consider the sizes 9, 9.5, 10, 10.5, 11, and 12. There are 6 size options in total.
Therefore, the number of favorable outcomes is 8 (for red color) × 6 (for size 9 or larger) = 48.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable Outcomes / Total Outcomes
Probability = 48 / 16
Probability = 3
Hence, the probability that a randomly chosen pair of shoes for the store display will be red and size 9 or larger is 3/16 or 0.1875 (approximately 18.75%).
P(red) = 1/2
How many sizes from 5-12?
How many from 9-12?
Now you can find P(size >= 9)
then just multiply that by 1/2