2. My friend takes 10 cards at random from a 52-card deck, and places them in a box. Then he puts the other 42 cards in a second, identical box. He hands me one of the two boxes and asks me to draw out the top card. What is the probability that the first card I draw will be the Ace of Spades?
Answers
Given : 10 cards at random taken from a 52-card deck, and placed in a box and 42 cards in other identical box . then top of the card is drawn from one of the box .
To find : Probability of card being Ace of Spades
Solution:
10 cards at random from a 52-card deck, and places them in a box.
probability that Ace of Spade is in that Box = 10/52 = 5/26
Probability of Ace of Spade in other box = 42/52 = 21/26
Probability of Selection o Box = 1/2 as Each box is identical
probability that the first card I draw will be the Ace of Spades
= (1/2) (1/42)(21/26) + (1/2)(1/10)(5/26)
= 1/104 + 1/104
= 1/52
probability that the first card I draw will be the Ace of Spades = 1/52
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