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Let A and B be independent events such...

Let A and B be independent events such that P(A) =0.6 and P(B ) =0.4.
find `P(A nn B) `

A

`0.24`

B

`0.76`

C

`0.56`

D

none of these

Text Solution

AI Generated Solution

The correct Answer is:
To find the probability of the intersection of two independent events A and B, we can use the formula: \[ P(A \cap B) = P(A) \times P(B) \] ### Step-by-Step Solution: 1. **Identify the probabilities of events A and B**: - Given: \( P(A) = 0.6 \) - Given: \( P(B) = 0.4 \) 2. **Use the formula for independent events**: - Since A and B are independent, we can calculate the probability of their intersection using the formula: \[ P(A \cap B) = P(A) \times P(B) \] 3. **Substitute the values into the formula**: \[ P(A \cap B) = 0.6 \times 0.4 \] 4. **Perform the multiplication**: \[ P(A \cap B) = 0.24 \] 5. **Conclusion**: - The probability of the intersection of events A and B is: \[ P(A \cap B) = 0.24 \]
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Knowledge Check

  • Let A and B be independent events such that P(A) =0.6 and P(B ) =0.4. find P (barA nn B )

    A
    `0.24`
    B
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    C
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    D
    none of these

  • Let A and B be independent events such that P(A) =0.6 and P(B ) =0.4. find P (barA nn barB)

    A
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    B
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    C
    `0.36`
    D
    `0.24`

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    A
    `0.24`
    B
    `0.76`
    C
    `0.36`
    D
    none of these

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