21. The probability of drawing an ace or a spade or both from a deck of cards is

- Option : B
- Explanation : Probability of drawing an ace from a deck of

52 cards = 4/52

Similarly the probability of drawing a card of

spades = 13/52

Probability of drawing an ace of spades = 1/52

Since two events (i.e. a card being an ace and a

card being of spades) are not mutually exclusive.

therefore

Probability of drawing an ace or a spade

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22. P(A_{1}' ∪ A_{2}' ∪ A_{3}') = 1 - P(A_{1}) P(A_{2}/A_{1}) P(A_{3}/A_{1} ∩ A_{2})

- Option : A
- Explanation :

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24. If A and B are independent and P (C) = 0, then A, B and C are independent,

- Option : A
- Explanation :

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- Option : B
- Explanation :
Let A be the event of getting 5 or 6

P(A) = 1/3 and B be the event of getting 1,2,3,4

P(B) = 2/3

In order to get a 'Head' before "5 or 6", the

following events have to occur:

H, TBH, TBTBH, TBTBTBH, ....

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