In a college, 4% of the men and 1% of the women are taller than 6 feet. Further more,
60% of the students are women. Now if a student is selected at random and is taller than
6 feet, what is the probability that the student is a women.
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To find the probability that a randomly selected student who is taller than 6 feet is a woman, we can use conditional probability. Let's break down the problem step by step:
Step 1: Define the events:
A: The student is a woman.
B: The student is taller than 6 feet.
Step 2: Determine the probabilities of each event:
P(A) = 60% (given: 60% of the students are women)
P(A') = 40% (the complement of P(A), which means P(not A))
P(B|A) = 1% (given: 1% of women are taller than 6 feet)
P(B|A') = 4% (given: 4% of men are taller than 6 feet)
Step 3: Apply the conditional probability formula:
The probability of event A given event B is calculated as:
P(A|B) = P(B|A) * P(A) / (P(B|A) * P(A) + P(B|A') * P(A'))
Substituting the given values:
P(A|B) = (1% * 60%) / ((1% * 60%) + (4% * 40%))
= 0.6 / (0.6 + 1.6)
= 0.6 / 2.2
≈ 0.273
Therefore, the probability that a randomly selected student who is taller than 6 feet is a woman is approximately 0.273, or 27.3%.
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