Question

If a person is randomly selected, find the probability that his or her birthday is not in may. Ignore leap years.

Answer 1

Calculate the probability:

We know, probability of an event $E$ is $\mathrm{P}\left(E\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}$

Let the probability of having birthday in May be $P\left(M\right)$ and probability of not having birthday in may be $P\left(M\right)\text{'}$

We know, the probability that an event will occur is equal to $1$ minus probability of that event will not occur.

Probability of of an event M, $P\left(M\right)=1-P\left(M\right)\text{'}$

Probability of having birthday in May, $P\left(M\right)=\frac{Numberofdaysinmay}{Numberofdaysinanyear}=\frac{31}{365}$

Probability of not having birthday in May, $P\left(M\right)\text{'}=1-P\left(M\right)$

$\Rightarrow P\left(M\right)\text{'}=1-\frac{31}{365}$

$\Rightarrow P\left(M\right)\text{'}=\frac{365-31}{365}$

$\Rightarrow P\left(M\right)\text{'}=\frac{334}{365}$

$\because$ Probability that his or her birthday is not in May = $\frac{334}{365}$.