If A and B are independent events such that P(A)=1/2, P(A B)=3/5 and P(B)=p, then value of p is: Option 1: 3/10 Option 2: 1/5 Option 3: 1/10 Option 4: 3/5

Answer: 1/5. Solution: For independent events, P(A B) = P(A) + P(B) - P(A)P(B). So 3/5 = 1/2 + p - p/2 = 1/2 + p/2. Thus p/2 = 1/10 and p = 1/5.

Algebra

Probability

Easy

core

If A and B are independent events such that $P(A)=\dfrac{1}{2}$ , $P(A\cup B)=\dfrac{3}{5}$ and $P(B)=p$ , then value of p is:

$\dfrac{3}{10}$

$\dfrac{1}{5}$

$\dfrac{1}{10}$

$\dfrac{3}{5}$

✅ Correct Option: 2

For independent events, $P(A\cup B) = P(A) + P(B) - P(A)P(B)$ .

So $\dfrac{3}{5} = \dfrac{1}{2} + p - \dfrac{p}{2} = \dfrac{1}{2} + \dfrac{p}{2}$ .

Thus $\dfrac{p}{2} = \dfrac{1}{10}$ and $p = \dfrac{1}{5}$ .

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If A and B are independent events such that P(A)=12P(A)=\dfrac{1}{2}P(A)=21​, P(A∪B)=35P(A\cup B)=\dfrac{3}{5}P(A∪B)=53​ and P(B)=pP(B)=pP(B)=p, then value of p is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If A and B are independent events such that $P(A)=\dfrac{1}{2}$ , $P(A\cup B)=\dfrac{3}{5}$ and $P(B)=p$ , then value of p is: