Question
Score: 0 of 1 point Data gathered on the shopping patterns during the months of April and May of high school students from Peanut Village revealed the following. \( 38 \% \) of students purchased a new pair of shorts (event H\( ), 15 \% \) of students purchased a new pair of sunglasses (event G ), and \( 6 \% \) of students purchased both a pair of shorts and a pair of sunglasses. Find the probability that a student purchased a pair of shorts given or purchased a new pair of sunglasses \( P(H \cup G)= \) Enter your answer
Ask by Macdonald Hamilton. in the United States
Feb 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability that a student purchased a pair of shorts or sunglasses is 0.47.
Solution
To find the probability that a student purchased a pair of shorts or purchased a pair of sunglasses (or both), we can use the formula for the union of two events:
P(H ∪ G) = P(H) + P(G) – P(H ∩ G)
We are given:
P(H) = 38% = 0.38
P(G) = 15% = 0.15
P(H ∩ G) = 6% = 0.06
Plugging these values into the formula:
P(H ∪ G) = 0.38 + 0.15 – 0.06 = 0.47
Therefore, the probability that a student purchased a pair of shorts or purchased a pair of sunglasses is 0.47 (or 47%).
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Simplify this solution The Deep Dive
To find the probability \( P(H \cup G) \), we can use the formula for the probability of the union of two events: \[ P(H \cup G) = P(H) + P(G) - P(H \cap G) \] Where: - \( P(H) = 38\% = 0.38 \) (the probability that a student purchased a new pair of shorts) - \( P(G) = 15\% = 0.15 \) (the probability that a student purchased a new pair of sunglasses) - \( P(H \cap G) = 6\% = 0.06 \) (the probability that a student purchased both) Now, substituting these values into the formula: \[ P(H \cup G) = 0.38 + 0.15 - 0.06 = 0.47 \] Therefore, the probability that a student purchased either a pair of shorts or a pair of sunglasses is \[ P(H \cup G) = 0.47 \]
