The probability that EM will offer you a free trip into space in the next month is 49%. Let this be P(A) where A is the event.

The probability that scientists from Area 51 will start selling pet aliens next month is 46%. Let this be P(B) where B is the event.

The probability that either EM will offer you a free trip to space or that scientists will begin sales of pet aliens next month is 31%. This is equal to the probability \(\displaystyle{P}{\left({A}\cap{B}\right)}\)

The probability that both EM will offer you a free trip into space and scientists from Area 51 will start selling pet aliens in the next month=? This is equivalent to \(\displaystyle{P}{\left({A}\cup{B}\right)}\)

Step 2

Now, by the formula,

\(\displaystyle{P}{\left({A}\cup{B}\right)}={P}{\left({A}\right)}+{P}{\left({B}\right)}-{P}{\left({A}\cap{B}\right)}\)

\(\displaystyle={0.49}+{0.46}-{0.31}\)

\(\displaystyle={0.64}\)

The answer is 64%.