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If A and B are two events 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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To determine whether events A and B are independent, we need to analyze the given probabilities and apply the definitions of independent events. ### Step-by-step Solution: 1. **Given Probabilities**: - \( P(A) = \frac{1}{2} \) - \( P(B) = \frac{7}{12} \) - \( P(\text{not } A \text{ or not } B) = \frac{1}{4} \) ...
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Knowledge Check

  • If A and B are events such that P(A)=(1)/(2), P(B) =(7)/(12) " and " P(A' uu B') =(1)/(4), then A and B are

    A
    independent
    B
    mutually exclusive
    C
    both `a` and `b`
    D
    none of these
  • NCERT-PROBABILITY-EXERCISE 13.2
    1. If A and B are two events such that P(A)=1/2, P(B) =7/(12)and P(not A...

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

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    3. Given that the events A and B are such that P (A) =1/2, P(AnnB)=3/5an...

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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) =1/2and P(AnnB)=...

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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 unbiased die are tossed. Let A be the event head a...

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

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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 tossed thrice. Find the probability of getting an odd number ...

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

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

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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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