Answer to Question #117879 in Statistics and Probability for Linda T

Question

The probability that a student belongs to a club is P(C)=0.4. The probability that a student works part time is P(PT)=0.5. The probability that a student belongs to a club AND works part time is P(C and PT)=0.05. What is the probability that a student belongs to a club OR works part time?

Answer 1

Solution:

Given,

The probability that a student belongs to a club is P(C)=0.4.

The probability that a student works part time is P(PT)=0.5.

The probability that a student belongs to a club AND works part time is P(C and PT)=0.05.

To find the probability that a student belongs to a club OR works part time,

means P(C ∪ PT)=?

P(C)=0.4,P(PT)=0.5,P(C ∩ PT)=0.05.

Using the formula P(C ∪ PT) = P(C) + P(PT) - P(C ∩ PT)

P(C ∪ PT) =0.4+0.5-0.05=[putting the values of P(C),P(PT), and P(C ∩ PT) ]

=0.9-0.05

=0.85

Answer. The probability that a student belongs to a club OR works part time is 0.85.