Question

According to the Chronicles of Contrived Statistics (March, 2016), the probability that Elon Musk will offer you a free trip into space in the next month is 41%. The probability that scientists from Area 51 will start selling pet aliens next month is 27%. Finally, the probability that either Elon Musk will offer you a free trip to space or that scientists will begin sales of pet aliens next month is 24%. What is the probability that both Elon Musk will offer you a free trip into space and scientists from Area 51 will start selling pet aliens in the next month?

Answer 1

`P(A\ and\ B) = 44\%`

Explanation:

Given

Represents the event as follows:

A =
`Elon\ Musk` will offer you a
`free\ trip` into space in the next month\

B = Scientists from
`Area\ 51` will
`start\ selling` pet aliens next month

So, we have:

`P(A) = 41\%`

`P(B) = 27\%`

`P(A\ or\ B) = 24\%`

Required

Determine
`P(A\ and\ B)`

This is calculated as:

`P(A\ and\ B) = P(A) + P(B) - P(A\ or\ B)`

So, we have:

`P(A\ and\ B) = 41\% + 27\% - 24\%`

`P(A\ and\ B) = 44\%`