Question

Given independent events A and B such that P(A) = 0.3 and P (B) = 0.5, which of the following is a correct statement?
(A) P(A/B) = 0

(B) P (B|A) = 0.3

(C) P(AB) = 0.5

(D) P(AUB) = 0.65

(E) P (AUB) = 0.80

Answer 1

Answer:

(D) P(AUB) = 0.65

Step-by-step explanation:

Since A and B are independent:

P(A ^ B)

= P(A) × P(B)

= 0.3 × 0.5 = 0.15

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

= 0.3 + 0.5 - 0.15

= 0.65

Answer 2

Answer:

Option C is correct $P(A\bigcup B)=0.65$

Step-by-step explanation:

Given information:

$P(A)=0.3\\P(B)=0.5$

From the theorem of conditional probability,

Independent events

$P(AB)=P(A)P(B)=0.3\times0.5=0.15$

$P(A/B)=\frac {P(A\bigcap B)}{P(B)}=P(A)=0.3$

$P(B/A)=\frac {P(B\bigcap A)}{P(A)}=P(B)=0.5$

$P(A\bigcup B)=P(A)+P(B)-P(A \bigcap B)=0.3+0.5-0.15=0.65$

Hence from above solution option C is correct $P(A\bigcup B)=0.65$

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