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If A and B are two events and P(A) = 0.3...

If `A and B` are two events and `P(A) = 0.3 , P(B) = 0.4 , P(A cap B) = 0.5` then `P(A cup B)` =

A

`0.5`

B

`0.2

C

1

D

`0.1`

Text Solution

AI Generated Solution

The correct Answer is:
To find the probability of the union of two events \( A \) and \( B \), we can use the formula: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Given: - \( P(A) = 0.3 \) - \( P(B) = 0.4 \) - \( P(A \cap B) = 0.5 \) Now, we can substitute these values into the formula: 1. **Substituting the values:** \[ P(A \cup B) = 0.3 + 0.4 - 0.5 \] 2. **Calculating the sum of \( P(A) \) and \( P(B) \):** \[ 0.3 + 0.4 = 0.7 \] 3. **Subtracting \( P(A \cap B) \):** \[ 0.7 - 0.5 = 0.2 \] Thus, the probability of the union of events \( A \) and \( B \) is: \[ P(A \cup B) = 0.2 \] ### Final Answer: \[ P(A \cup B) = 0.2 \]
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Knowledge Check

  • If A and B are two events such that P(A) =0.2 , P(B) = 0.4 and P( A cup B) = 0.6 then P(A/B) is equal to

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    B
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    A
    `1/10`
    B
    `3/10`
    C
    `6/7`
    D
    `3/8`

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    A
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    B
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    C
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    D
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