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Events A and B are such that P(A)=1//2,P...

Events A and B are such that `P(A)=1//2,P(B)=7//12,` and P (not A or not B) = 1/4. State whether A and B are independent ?

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If A and B are mutually exclusive
P (not A or not B) = `1/4` i.e.
By substituting the values
`P (A ∩ B) = 1 – 1/4 = 3/4 …… (1)`
For two mutually exclusive events
`P (A ∩ B) = 0` but here `P (A ∩ B) ≠ 0`
Hence, A and B are not mutually exclusive.
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NCERT ENGLISH-PROBABILITY-EXERCISE 13.2
  1. Events A and B are such that P(A)=1//2,P(B)=7//12, and P (not A or not...

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  2. One card is drawn at random from a well shuffled deck of 52 cards. I...

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  3. Given that the events E and F are such that P(E) = (1)/(2), P(E cup F)...

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  4. A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be ...

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  5. If A and B are two events such that P(A)=1/4, P(B)=1/2a n d\ P(AnnB)=1...

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  6. Let A and B be independent events with P(A) = 0. 3and P(B) = 0. 4Find...

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  7. Let E and F be events with P (E) =3/5, P (F) =3/(10)and P(EnnF)=1/5. A...

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  8. If P(A) =3/5and P(B) =1/5, find P(AnnB)if A and B are independent even...

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  9. A fair coin and an in biased die are tossed. Let A be the event head ...

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  10. A box of oranges is inspected by examining g three randomly selected ...

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  11. Two cards are drawn at random and without replacement from a pack of ...

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  12. Two events A and B will be independent, if(A) A and B are mutually ex...

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  13. Given two independent events A and B such thatP(A) = 0. 3,P(B) = 0. 6...

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  14. A die is thrown thrice. Find the probability of getting an odd number ...

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  15. Two balls are drawn at a random with replacement from a box contain...

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  16. Probability of solving specific problem independently by A and B are 1...

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  17. In a hostel 60% of the students read Hindi news paper, 40% read Engli...

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  18. The probability of obtaining an even prime number on each die, when a...

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