Given two independent events A and B such that P (A) = 0.3, P (B) = 0.6. Find (i) P (A and B) (ii) P (A and not B) (iii) P (A or B) (iv) P (neither A nor B)
(i)
The probability of A is 0 ⋅ 3 and the probability of B is 0 ⋅ 6 .
The formula for two independent events is,
P ( A ∩ B ) = P ( A ) ⋅ P ( B )
Substitute the given values in the above formula we get,
P ( A ∩ B ) = 0 ⋅ 3 × 0 ⋅ 6 = 0 ⋅ 18
Thus, the value of P ( A ∩ B ) = 0 ⋅ 18 .
(ii)
The probability of ( A and not B ) or P ( A ∩ B' ) is,
P ( A ∩ B ′ ) = P ( A ) − P ( A ∩ B ) = 0.3 − 0.18 = 0.12
Thus, the value of P ( A ∩ B' ) = 0.12 .
(iii)
The formula of P ( A ∪ B ) is,
P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B )
Substitute the given values in the above formula we get,
P ( A ∪ B ) = 0.3 + 0.6 − 0.18 = 0.9 − 0.18 = 0.72
Thus, the value of P ( A ∪ B ) = 0.72 .
(iv)
The formula probability of (neither A nor B ) or P ( A ′ ∩ B ′ ) is,
P ( A ′ ∩ B ′ ) = P ( A ∪ B ) ′ = 1 − P ( A ∪ B )
Substitute the given values in the above formula we get,
P ( A ′ ∩ B ′ ) = 1 − 0.72 = 0.28
Thus, the value of P ( A ′ ∩ B ′ ) = 0.28 .
(i)
The probability of
The formula for two independent events is,
Substitute the given values in the above formula we get,
Thus, the value of
(ii)
The probability of (
Thus, the value of
(iii)
The formula of
Substitute the given values in the above formula we get,
Thus, the value of
(iv)
The formula probability of (neither
Substitute the given values in the above formula we get,
Thus, the value of
