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

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

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

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

A - (B capC) = (A - B) cap (A-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 P(B)= (3)/(5), P(A//B)= (1)/(2) and P(A cup B)= (4)/(5) then P(A cup B)' + P(A' cup 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') = ……….

If A and B are two events such that P(A | B)= p, P(A) = p, P(B)= (1)/(3) and P(A cup B) = (5)/(9) then p = ……….

For events A and B P(bar(A cup B))= (1)/(6), P(barA)= (1)/(4) and P(A cap B) = (1)/(4) , Where (barA) is the complementary event of A then events A and B are

The set (A cap B')' cup (B cap C) is equal to

P(A' cup B') | C = ………………

KUMAR PRAKASHAN-PROBABILITY-Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. A discrete random variable X has the probability distribution given as...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. A dice is thrown three times. Let X be 'the number of two seen'. Find ...

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