Q:

In which example are the events independent? A) Ariel has a standard deck of 52 cards. She draws one card from the deck and then replaces it. She then draws a second card from the deck. What is the probability that both cards are clubs? B) Alisa has a bag of 10 red and 6 green marbles. She takes one marble out of the bag and does not replace it. She then takes a second marble out of the bag. What is the probability that both marbles are green? C) In a bag of apples there are 4 green apples and 2 red apples. Bethany takes a green apple out of the bag and does not replace it. She then takes another apple out of the bag. What is the probability that the second apple is red? D) In Mrs. Brown's Geometry class there are 15 boys and 10 girls. The students are presenting projects to the class. If Mrs. Brown selects students at random for presentations, what is the probability that the first 2 students chosen are girls?

Accepted Solution

A:
A) 1/16
B) 1/8
C) 4/15
D) 3/20

For A, there are 13 clubs out of 52 cards.  Since the card is replaced, the probability that the second card is a club is also 13/52:
13/52(13/52) = 169/2704 = 1/16

For B, there are 6 green marbles out of 16.  Since the marble is not replaced, the probability that the second marble is green is 5/15:
6/16(5/15) = 30/240 = 1/8

For C, there are 4 green apples out of 6.  Since the apple is not replaced, the probability that the second apple is red is 2/5:
4/6(2/5) = 8/30 = 4/15

For D, there are 10 girls out of 25 students.  Since we are choosing 2 separate students, the probability of the second girl is 9/24:
10/25(9/24) = 90/600 = 3/20