Question

two cards are drawn from a well shuffled pack of 52 cards and these cards thrown away.what is the probability of getting an ace from the left 50 cards

Answer 1

Number of cards in a deck = 52 (Given)

First two cards removed are not ace:

P(Drawing an ace) = P(first card ≠ ace, second card ≠ ace, third card = ace)

P(Drawing an ace) =  (48/52)(47/51)(4/50) = 376/5525

One of the first two cards removed is an ace:

P(Drawing an ace) = P(first or second card = ace, third card = ace)

P(Drawing an ace) = 2 [ (48)(52)(4/51)(3/50) ]  = 48/5525

First two cards removed are both aces:

P(Drawing an ace) = P(All 3 cards are ace)

P(Drawing an ace) =  (4)(52)(3/51)(2/50)  = 1/5525

Find the probability of drawing an ace from the deck:

P(Drawing an ace from the 50 cards) = 376/5525 + 48/5525 + 1/5525

P(Drawing an ace from the 50 cards) = 425/5525

P(Drawing an ace from the 50 cards) = 1/13

Answer: 1/3