Question

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.

Answer 1

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`