Question

If P(A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find
(i) P(A ∩ B)
(ii) P(A|B)
(iii) P(A ∪ B)

Answer 1

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1)P(AnB)

GIVEN,
P(A)=O.8. P(B)=0.5. P(B/A)=0.4

WE KNOW THAT,

P(B/A)=P(AnB)/P(A)

0.4=P(AnB)/0.8

0.4×0.8=P(AnB)

0.32=P(AnB).

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2)P(A/B)

WE KNOW THAT,

P(A/B)=P(AnB)/P(B)

P(A/B)=0.32/0.5

P(A/B)=32/50

P(A/B)=16/25

P(A/B)=0.64.

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3)P(AUB)

WE KNOW THAT,

P(AUB)=P(A)+P(B)-P(AnB)

=0.8+0.5-0.32

=1.3-0.32

=0.98.

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Answer 2

The value of P(A ∩ B) is 0.32

The value of P(A|B) is 0.64

The value of P(A ∪ B) is 0.98

Step-by-step explanation:

Consider the provided information.

P(A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4

Part (i): P(A ∩ B)

Use the formula: $P(B|A)=\frac{P(B\cap A)}{P(A)}$

Substitute the respective values in the above formula.

$0.4=\frac{P(B\cap A)}{0.8}$

$P(B\cap A)=0.32$

Hence, the value of P(A ∩ B) is 0.32

Part (ii) P(A|B)

Use the formula: $P(A|B)=\frac{P(A\cap B)}{P(B)}$

Substitute the respective values in the above formula.

$P(A|B)=\frac{P(0.32)}{0.5}$

$P(A|B)=0.64$

Hence, the value of P(A|B) is 0.64

Part (iii) P(A ∪ B)

Use the formula: P(A ∪ B) = P(A)+P(B)-P(A∩ B)

Substitute the respective values in the above formula.

P(A ∪ B) = 0.8+0.5-0.32

P(A ∪ B) = 0.98

Hence, the value of P(A ∪ B) is 0.98

#Learn more

Question 7 A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A∩B) = 0.35.

Find (i) P(A∩B) (ii) P(A′∩B′) (iii) P(A∩B′) (iv) P(B∩A′)

https://brainly.in/question/1842395