Question

 If A and B are two independent events with P(A)=0.8 and P(B)=0.7, What is the value of P(AUB)?​

Answer 1

Please find the attachment

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

1. Two events A and B are said to be mutually independent if

$\sf{P(A \: \cap \: B) = P(A) P(B)}$

2. For two events A & B

$\sf{P(A \cup \: B) = P(A) + P(B) - P(A \cap \: B)}$

GIVEN

A and B are two independent events with

P(A)=0.8 and P(B)=0.7

TO DETERMINE

The value of P(AUB)

CALCULATION

For two events A & B

$\sf{P(A \cup \: B) = P(A) + P(B) - P(A \cap \: B)}$

Since A & B are independent

We get from above

$\sf{P(A \cup \: B) = P(A) + P(B) - P(A) \:P( B)}$

$\implies \: \sf{P(A \cup \: B) =0.8 + 0.7 - (0.8 \times 0.7)}$

$\implies \: \sf{P(A \cup \: B) =1.5 -0.56}$

$\implies \: \sf{P(A \cup \: B) =0.94}$

RESULT

$\boxed{ \: \: \: \sf{P(A \cup \: B) =0.94 \: \: } \: }$

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