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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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Most popular questions from this chapter

Use the following information to answer the next two exercises. You see a game at a local fair. You have to throw a dart at a color wheel. Each section on the color wheel is equal in area.

Let B = the event of landing on blue.

Let R = the event of landing on red.

Let G = the event of landing on green.

Let Y = the event of landing on yellow.

If you land on Y, you get the biggest prize. Find P(Y).

A box has two balls, one white and one red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Find the probability of the following events:

a. Let F = the event of getting the white ball twice.

b. Let G = the event of getting two balls of different colors.

c. Let H = the event of getting white on the first pick.

d. Are F and G mutually exclusive?

e. Are G and H mutually exclusive?

Write the symbols for the probability that a player is an outfielder and is a great hitter.

Write the symbols for the probability that a player is a great hitter, given that the player is an infielder.

In a box of assorted cookies, 36%contain chocolate and 12%contain nuts. Of those, 8%contain both chocolate and nuts. Sean is allergic to both chocolate and nuts.

a. Find the probability that a cookie contains chocolate or nuts (he can't eat it).

b. Find the probability that a cookie does not contain chocolate or nuts (he can eat it).
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