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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.

1 Answer

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Answer:
P\left ( A\right )=0.45


P\left ( B\right )=0.32

Explanation:

Given


P\left ( A\cup B\right )=0.626


P\left ( A\cap B\right )=0.144

and we know


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


0.626=P\left ( A\right )+P\left ( B\right )-0.144


0.77=P\left ( A\right )+P\left ( B\right )-------1

as it is given

A and B are independent therefore


P\left ( A\cap B\right )=P\left ( A\right )\cdot P\left ( B\right )


0.144=P\left ( A\right )\cdot P\left ( B\right )

Substitute value of
P\left ( B\right ) in 1


0.77=P\left ( A\right )+(0.144)/(P\left ( A\right ))

on solving
P\left ( A\right )=0.45


P\left ( B\right )=0.32

User Rob Raymond
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