Compound Probability Without Replacement

A basket contains 5 purple pencils and 9 brown pencils. If two pencils are picked at random one after the other with replacement, then what is the probability that both the pencils are purple?

• 9/182

• 5/182

• 25/196

• 10/91

There are 6 red marbles, 5 green marbles, and 4 yellow marbles in a bag. If Joe picks 2 marbles one after the other without replacement, then what is the probability that both are red in color?

• 2/5
• 1/21
• 4/25
• 1/7

A magician is doing a card trick using a standard deck of cards. What is the probability that he will pull a jack, followed by a queen? Assume he does NOT put the jack back. 
(Hint: there are 4 jacks and 4 queens in the deck of 52 total cards)

• 1/13
• 4/663
• 4/13
• 1/104

Each of the letters in MATHEMATICS are on separate cards, face down on a table. If you pick a card at random, and then another card with replacement what is the probability that both card will be a vowel?

• 4/11

• 16/121

• 7/21

• 6/55

A bag contains ten black bows, twenty white bows, and 5 grey bows. If Ms. Sedlock picks one without looking, what is the probability she chooses a black, white, and grey bow? Assume she puts the bow back each time. 

• 8/343
• 35/100
• 4/257
• 3/49

A bag contains 2 blue marbles, 3 black marbles, and 5 red marbles. If Mrs. Grow pulls two marbles without replacement, what is the probability of them both being blue? 

• 1/45
• 1/5
• 1/20
• 2/5