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

$P\left ( B\right )=0.32$

Step-by-step 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

$0.77=P\left ( A\right )+\frac{0.144}{P\left ( A\right )}$

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

$P\left ( B\right )=0.32$