Question

if p(a)=2/3,p(b)=1/5, prove that 2/15≤ p(ab)≤ 1/5
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Answer 1

Given:

if p(a)=2/3,p(b)=1/5.

To Prove:

2/15≤ p(ab)≤ 1/5  .

Solution:

Since, we know that-

A conditional probability is the probability of one event if another event occurred.

here, given that- p(a)=2/3, p(b)=1/5  is example of conditional probability.

therefore, p(a/b)=p(a)

Since, for conditional probability;

$p(a/b)=\dfrac{p(ab)}{p(b)}\\\\\Rightarrow p(a)=\dfrac{p(ab)}{p(b)}\\\\\Rightarrow p(ab)=p(a)\times p(b)\\\Rightarrow p(ab)=(2/3)\times(1/5)\\\Rightarrow p(ab)=2/15$

since, $2/15\leq 1/5 \ and \ p(ab)=2/15$

this implies;

$2/15=p(ab)\leq1/5\\\\\Rightarrow 2/15\leq p(ab)\leq 1/5$

Hence, proved.