Question

Suppose () = 46%; ( and ) = 10%; and ( or ) = 62% Find (Not ). Can this really be a probability? If not, explain why not.

Answer 1

`P(E) = 26 \%`

Explanation:

Given

`P(F) = 46\%`

`P(E\ and\ F) = 10\%`

`P(E\ or\ F) = 62\%`

Required

Find P(E)

In probability:

`P(E\ and\ F) = P(E) + P(F) - p(E\ or\ F)`

Substitute the right values

`10\% = P(E) + 46\% - 62\%`

`10\% = P(E) -16 \%`

Collect Like Terms

`P(E) = 10\% +16 \%`

`P(E) = 26 \%`

It is a probability because all probabilities are within the range 0 to 100%