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If two events are independent, then...

If two events are independent, then

A

they must be mutually exclusive

B

the sum of their probabilities must be equal to 1

C

Both (a) and (b) are correct

D

none of the above is correct

Text Solution

Verified by Experts

If two events A and B are independent, then we knpw that
`P(AcapB)=P(A)cdotP(B),P(A)ne0,P(B)ne0`
`Since,m a nd B have a common outcome
Further, mutually exlusive events never have a common outcome.
In other words, two independent eevnts having non-zeroprobabilities of occurrence cannot be mutuallyexclusive events having non-zero probabilitiesof outcome cannot be independent.
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Knowledge Check

  • A and B try to hit a target. The probability that A hits the target is 7/10 and the probability that B hits the target is 4/10. If these two events are independent, the probability that B hits the target, given that the target is hit,is :

    A
    `17//41`
    B
    `20//41`
    C
    `19//41`
    D
    `18//41`

  • Two events E and F are independent. If P(E )=0.3 and P(EcupF)=0.5 then P(E//F)-P(F//E) equals to

    A
    `2/7`
    B
    `3/35`
    C
    `1/70`
    D
    `1/7`

  • If A' , B' are complementary events of two independent events A, B, then P(Acup B) =

    A
    `1-P(A) P(B')`
    B
    `1 - P(A') P(B)`
    C
    `1-P(A')P(B')`
    D
    `P(A')+P(B')`

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