Question

Please solve this question;
if A and B are two events such that P(AUB)=5/6, P(A)=1/2 AND P(B)=2/3 Show that A and B are independent.

Answer 1

SOLUTION

GIVEN

A and B are two events such that P(AUB)=5/6, P(A)=1/2 AND P(B)=2/3

TO PROVE

A and B are independent.

EVALUATION

Here it is given that A and B are two events such that P(AUB)=5/6, P(A)=1/2 and P(B)=2/3

We are aware of the formula on probability that

P(A∪B) = P(A) + P(B) - P(A∩B)

$\displaystyle \implies \sf{ \frac{5}{6} = \frac{1}{2} + \frac{2}{3} - P(A \cap B)}$

$\displaystyle \implies \sf{ \frac{5}{6} = \frac{3 + 4}{6} - P(A \cap B)}$

$\displaystyle \implies \sf{ \frac{5}{6} = \frac{7}{6} - P(A \cap B)}$

$\displaystyle \implies \sf{ P(A \cap B) = \frac{2}{6} }$

$\displaystyle \implies \sf{ P(A \cap B) = \frac{1}{2} \times \frac{2}{3} }$

$\displaystyle \implies \sf{ P(A \cap B) = P(A ) \times P(B) }$

Hence A and B are independent

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. among 21 components 3 are defective. what is the probability that a component selected at random is not defective

https://brainly.in/question/22719974

2. The sun rises from north. What is the probability

https://brainly.in/question/25984474