Of all the Sunny Club members in a particular city, 25% prefer swimming on weekends and 75% prefer swimming on weekdays. It is f

Question

1 month ago

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Of all the Sunny Club members in a particular city, 25% prefer swimming on weekends and 75% prefer swimming on weekdays. It is f

ound that 10% of the members in that city prefer swimming on weekends and are female, while 55% of the members in that city prefer swimming on weekdays and are female. The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is . NextReset

Mathematics

2 answers:

Svet_ta [12.7K] · Answer 1 · 2026-02-25T05:01:40+03:00

Answer: The likelihood that a randomly selected club member is female, assuming the individual enjoys swimming on weekends, is 40%.

Step-by-step explanation:

Let E₁ represent the scenario where members favor weekend swimming.

Let E₂ denote the scenario where members favor weekday swimming.

Let A signify the event that members are female.

The probability that members prefer weekend swimming P(E₁) is 25%.

The probability for members who prefer weekday swimming P(E₂) is 75%.

The probability of members who are female and prefer weekend swimming P(A∩E₁) is 10%.

The probability of female members who prefer weekday swimming P(A∩E₂) is 55%.

To determine the probability of a member being female when they prefer weekend swimming, we apply the Conditional theorem.

$P(A\mid E_1)=\dfrac{P(A\cap E_1)}{P(E_1)}\\\\P(A\mid E_1)=\dfrac{10}{25}\\\\P(A\mid E_1)=0.4\\\\P(A\mid E_1)=0.4\times 100\%=40\%$

Thus, the chance that a randomly chosen club member is female, provided they like swimming on weekends, is 40%.

Leona [12.6K] · Answer 2 · 2026-02-25T05:03:02+03:00

Leona [12.6K]1 month ago

3 0

P(f | weekend) = p(f & weekend)/p(weekend)
.. = 10%/25%
.. = 0.4 = 2/5