Let E and F are two independent events such that P(E)=0.35 and P(E F)=0.60 then which of following statements are TRUE? (A) P(F)=5/13 (B) P(E, F)=0.35 (C) P(E, F)=0.65 (D) P(E, F)=0.65 Choose the correct answer from the options given below: Option 1: (A) and (B) only Option 2: (A) and (C) only Option 3: (A), (B) and (D) only Option 4: (A) and (D) only

Answer: (A), (B) and (D) only. Solution: Independence gives 0.60=0.35+P(F)-0.35P(F), so P(F)=0.25/0.65=5/13 and (A) is true. Independence also makes P(E, F)=P(E)=0.35 and P( E, F)=P( E)=0.65, so (B) and (D) are true while (C) is false.

Algebra

Probability

Medium

core

Let E and F are two independent events such that $P(E)=0.35$ and $P(E\cup F)=0.60$ then which of following statements are TRUE?

(A) $P(F)=\frac{5}{13}$

(B) $P(E|\overline{F})=0.35$

(C) $P(E|\overline{F})=0.65$

(D) $P(\overline{E}|\overline{F})=0.65$

Choose the correct answer from the options given below:

(A) and (B) only

(A) and (C) only

(A), (B) and (D) only

(A) and (D) only

✅ Correct Option: 3

Independence gives $0.60=0.35+P(F)-0.35P(F)$ , so $P(F)=\frac{0.25}{0.65}=\frac{5}{13}$ and (A) is true.

Independence also makes $P(E|\overline F)=P(E)=0.35$ and $P(\overline E|\overline F)=P(\overline E)=0.65$ , so (B) and (D) are true while (C) is false.

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Solution

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