Question

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

Answer 1

Answer: There is a probability that a club member picked randomly is female, given that the person prefers swimming on weekends is 40%.

Step-by-step explanation:

Let E₁ be the event that members prefer swimming on weekends.

Let E₂ be the event that members prefer swimming on weekdays.

Let A be the event that the members are female.

Probability that members prefer swimming on weekends P(E₁) = 25%

Probability that members prefer swimming on weekdays P(E₂)= 75%

Probability that members prefer swimming on weekends and are female PA∩E₁)= 10%

Probability that members prefer swimming on weekdays and are female P(A∩E₂) = 55%

Using Conditional theorem, we will find the probability that a member is female given that the the person prefers swimming on weekends.

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

Hence, there is a probability that a club member picked randomly is female, given that the person prefers swimming on weekends is 40%.

Answer 2

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