Question

In a college, 50% are blondes, 10% have green eyes, and 3% are blondes that have green eyes. What is the probability that a student selected will be a blonde or have green eyes?

Answer 1

The probability that events A or B occur is the probability of the union of A and B.

Similarly, the probability that events A and B occur is the probability of the intersection of A and B.

The probability of the union of two events is:

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

In this case, we have:

`P(\text{blonde or green eyes})=P(\text{blonde})+P(\text{green eyes})-P(\text{blonde and green eyes})`
`\begin{gathered} P(\text{blonde})=50\text{\% }=(50)/(100)=0.5 \\ P(\text{green eyes})=10\text{\% }=(10)/(100)=0.1 \\ P(\text{blonde and green eyes})=3\text{\% }=(3)/(100)=0.03 \\ P(\text{blonde or green eyes})=P(\text{blonde})+P(\text{green eyes})-P(\text{blonde and green eyes}) \\ P(\text{blonde or green eyes})=0.5+0.1+0.03 \\ P(\text{blonde or green eyes})=0.57 \end{gathered}`

Therefore, the probability that a student selected will be blonde or have green eyes is 0.57 or 57%.