One satellite is scheduled to be launched from Cape Canaveral in Florida, and another launching is scheduled for Vandenberg Air Force Base in California. Let A denote the event that the Vandenberg launch goes off on schedule, and let B represent the event that the Cape Canaveral launch goes off on schedule. If A and B are independent events with P(A) > P(B), P(A ∪ B) 5 .626, and P(A ∩ B) 5 .144, determine the values of P(A) and P(B) to three decimal places.

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nuuk nuuk · Answer 1 · 2019-10-16T10:49:49+02:00

Answer:[tex]P\left ( A\right )=0.45[/tex]

[tex]P\left ( B\right )=0.32[/tex]

Step-by-step explanation:

Given

[tex]P\left ( A\cup B\right )=0.626[/tex]

[tex]P\left ( A\cap B\right )=0.144[/tex]

and we know

[tex]P\left ( A\cup B\right )=P\left ( A\right )+P\left ( B\right )-P\left ( A\cap B\right )[/tex]

[tex]0.626=P\left ( A\right )+P\left ( B\right )-0.144[/tex]

[tex]0.77=P\left ( A\right )+P\left ( B\right )[/tex]-------1

as it is given

A and B are independent therefore

[tex]P\left ( A\cap B\right )=P\left ( A\right )\cdot P\left ( B\right )[/tex]

[tex]0.144=P\left ( A\right )\cdot P\left ( B\right )[/tex]

Substitute value of [tex]P\left ( B\right )[/tex] in 1

[tex]0.77=P\left ( A\right )+\frac{0.144}{P\left ( A\right )}[/tex]

on solving [tex]P\left ( A\right )=0.45[/tex]

[tex]P\left ( B\right )=0.32[/tex]