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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?

Sagot :

MrRoyalidn

Answer:

[tex]P(A\ and\ B) = 44\%[/tex]

Step-by-step explanation:

Given

Represents the event as follows:

A = [tex]Elon\ Musk[/tex] will offer you a [tex]free\ trip[/tex] into space in the next month\

B = Scientists from [tex]Area\ 51[/tex] will [tex]start\ selling[/tex] pet aliens next month

So, we have:

[tex]P(A) = 41\%[/tex]

[tex]P(B) = 27\%[/tex]

[tex]P(A\ or\ B) = 24\%[/tex]

Required

Determine [tex]P(A\ and\ B)[/tex]

This is calculated as:

[tex]P(A\ and\ B) = P(A) + P(B) - P(A\ or\ B)[/tex]

So, we have:

[tex]P(A\ and\ B) = 41\% + 27\% - 24\%[/tex]

[tex]P(A\ and\ B) = 44\%[/tex]

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