According to the Chronicles of Contrived Statistics (March, 2016), the

TokNeekCepTdh 2021-11-21 Answered
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 49%. The probability that scientists from Area 51 will start selling pet aliens next month is 46%. 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 31%. 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?

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Expert Answer

oces3y
Answered 2021-11-22 Author has 57 answers
Step 1
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%.
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