In a group of 30 students 12 students like pizza 13 students like burgers and five students like both pizza and burgers if a student is choosing at random what is the probability that the student likes either pizza or burgers?
To find the probability that a student likes either pizza or burgers, we can use the principle of inclusion and exclusion.
Let A be the event that a student likes pizza and B be the event that a student likes burgers. The probability of a student liking either pizza or burgers can be calculated using the formula:
P(A or B) = P(A) + P(B) - P(A and B)
Given that 12 students like pizza, 13 students like burgers, and 5 students like both pizza and burgers, we can plug in the values:
P(A) = 12/30 = 0.4
P(B) = 13/30 = 0.4333
P(A and B) = 5/30 = 0.1667
Therefore,
P(A or B) = 0.4 + 0.4333 - 0.1667
P(A or B) = 0.6666
So, the probability that a student likes either pizza or burgers is 0.6666 or approximately 66.67%.