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Prove that, P(A)=P(A cap B) +P(A cap ...

Prove that,
` P(A)=P(A cap B) +P(A cap barB)`

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Prove that P(A cup B) = P(A cap B)+P(A cap barB)+P(barA cap B)

If A, B and C be sets. Then, show that, A cap (B cup C) = (A cap B) cup (A cap C) .

If A and B are two independent events such that P(A cap B)= (3)/(25) and P(A' cap B)= (8)/(25) , then P(B)= ……….

If two events A and B are such that P(A')= 0.3, P(B)=0.5 and P(A cap B) = 0.3 , then P(B | A cup B') is …………

A and B are events such that P(A')= 0.3, P(B) = 0.4 and P(A cap B') = 0.5 then P[B | (A cup B')] = …………

A and B are events such that P(A)= 0.4, P(B)= 0.3 and P(A cup B)= 0.5 . Then P(B' cap A') equal = ……..

Given that the events A and B are such that P(A)= (1)/(2), P( A cap B)= (3)/(5) . And P(B )= p. Find p if they are (i) mutually exclusive (ii) independent.

For any two sets A and B, prove that A cup B= A cap B iff A = B .

If A and B are events such that P(A' cup B') = (2)/(3) and P(A cup B) = (5)/(9) , then P(A') + P(B') = ……….

KUMAR PRAKASHAN-PROBABILITY-Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. Let E(1) and E(2) be two independent events such that P(E(1)) = P(1) a...

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  2. A discrete random variable X has the probability distribution given as...

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  3. Prove that, P(A)=P(A cap B) +P(A cap barB)

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  4. Prove that P(A cup B) = P(A cap B)+P(A cap barB)+P(barA cap B)

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  5. If X is the number of tails in three tosses of a coin, determine the s...

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  6. In a dice game, a player pays a stake of ₹ 1 for each throw of a die. ...

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  7. Three dice are thrown at the sametime. Find the probability of getting...

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  8. Suppose 10,000 tickets are sold in a lottery each for ₹ 1. First prize...

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  9. A bag contains 4 white and 5 black balls. Another bag contains 9 white...

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  10. Bag-I contains 3 black and 2 white balls, Bag-II contains 2 black and ...

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  11. A box has 5 blue and 4 red balls. One ball is drawn at random and not ...

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  12. Four cards are successively drawn without replacement from a deck of 5...

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  13. If a die is thrown 5 times. Then find the probability that an odd numb...

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  14. Ten coins are tossed. Then what is the probability of getting atleast ...

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  15. The probability of a man hitting a target is 0.25. He shoots 7 times, ...

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  16. A lot of 100 watches is known to have 10 defective watches. If 8 watch...

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  17. Consider the probability distribution of a random variable X: Cal...

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  18. The probability distribution of a random variable X is given below: ...

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  19. For the following probability distribution determine standard deviatio...

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  20. A biased die is such that P(4) = (1)/(10) and other scores being equal...

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