Question

Given two events A and B of a sample set where P[A] = .20 P[not B] = .40 P[B|A] = .25 What is P[A or B]?

Answer 1

Answer:

Given two events A and B of a sample set :-

P[A] = 0.20  

P[not B]=0.40

$P[B/A]=0.25$

To find P[A or B]:

$P[A or B] = P[A] + P[B] - P[A \cap B]$                ......[1]

Calculate for $P[B]$ and $P[A \cap B]$

P[B] = 1- P[not B]

Substitute the value P[not B] we get;

P[B] = 1-0.40 = 0.60      

$P[A \cap B] = P[B/A] \cdot P[A]$

Substitute the given values we get;

$P[A \cap B] = 0.25 \cdot 0.20 = 0.05$

Then;

$P[A or B] = 0.20+0.60-0.05 = 0.80-0.05 =0.75$

Therefore, the value of P[A or B] is, 0.75.