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Chapter 3: Q3.6 (page 183)

Draw two cards from a standard 52-card deck with replacement. Find the probability of getting at least one black card.

Short Answer

Expert verified

Probability of getting at least one black card = 3/4 or 0.75

Step by step solution

01

Basics 

A standard deck of 52 cards contains 26 red & 26 black cards. So, probability of getting a black or a red card in single draw is equal, ie 26/52 = 1/2 each.

With replacement means that the card first drawn is again put into the deck before the second draw.

02

Explanation & Solution 

As Probability of getting a red card = 26/52 = 1/2

With replacement, probability of getting second red card also = 26/52 = 1/2

  • Probability of getting at least one black card = 1 - Pr (Getting both red cards)

So, Pr (At least one black card) = 1 - ( 1/2 x 1/2 )

= 1 - 1/4

Hence, probability = 3/4

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