Practice with Conditional Probability Topic Index | Algebra Index | Regents Exam Prep Center

Answer the following questions dealing with conditional probability.

 1. You roll two dice.  The first die shows a ONE and the other die rolls under the table and you cannot see it.  Now, what is the probability that both die show ONE? Choose: 1 : 3 1 : 6 1 : 36 9 : 36 Answer Since you already know that one of the dice shows a ONE, the probability of getting a ONE on the other die is 1 out of 6.

 2. You decide to tell your fortune by drawing two cards from a standard deck of 52 cards.  What is the probability of drawing two cards of the same suite in a row?  The cards are not replaced in the deck. Choose: 13/52 12/51 13/51 12/52 Answer Here is an example of what might happen: The first card you draw is a heart. There are now 51 cards left. There are 12 hearts left in the deck. The probability of another heart is 12 out of 51. Since the number of cards in each suite is the same, 13, the answer will be the same regardless of which suite you draw first.

 3. A new bag of golf tees contains 10 red tees, 10 orange tees, 10 green tees and 10 blue tees.  You empty the tees into your golf bag.  What is the probability of grabbing out two tees of the same color in a row for you and your partner? Choose:  1/40 10/40 9/39 9/40 Answer You grab a tee and it is red. (The tee you grab could be any color. Red is used here as an example.) (The answer will be the same regardless of the color of the tee you grab.) There are now 39 tees remaining in the bag. There are 9 red tees remaining in the bag. The probability of drawing another red is 9 out of 39.

 4. In a library box, there are 8 novels, 8 biographies, and 8 war history books.  If Jack selects two books at random, what is the probability of selecting two different kinds of books in a row? Choose: 16/23 16/24 8/24 7/23 Answer Here is an example of what might happen: Jack selects a book and it is a novel. There are 23 books remaining in the box. There are 16 books remaining that are not novels. Probability of NOT a novel is 16 out of 23. The answer will remain the same regardless of the first book chosen by Jack since there are 8 copies of each style book.

 5. What is the probability that the sum of two die will be greater than 8, given that the first die is 6? Choose: 1/2 3/4 2/3 7/12 Answer Consider your choices. If the first die is 6, you could have: (6,1), (6,2), (6,3), (6,4), (6.5), (6,6) but you need the sum to be >8, so you have: (6,3), (6,4), (6,5), (6,6). There are 4 answers out of 6 choices. Probability: 4/6 or 2/3

 6. What is the probability of drawing two aces from a standard deck of cards, given that the first card is an ace? The cards are not returned to the deck. Choose: 1/663 1/221 4/52 3/51 Answer There are 4 aces in a standard deck of 52 cards. If one ace is drawn, this leaves 3 aces in the remaining 51 cards. The probability of drawing a second ace: 3/51

 7. A new superman MasterCard has been issued to 2000 customers.  Of these customers, 1500 hold a Visa card, 500 hold an American Express card and 40 hold a Visa card and an American Express card.  Find the probability that a customer chosen at random holds a Visa card, given that the customer holds an American Express card. Choose: 1/4 1/3 2/25 1/50 Answer n(A) = American Express = 500 n(A and B) = both = 40 Formula: P(B|A)=P(A and B)/P(A) P(B|A)=40/500 = 2/25

8.

A survey of middle school students asked:  What is your favorite winter sport?  The results are summarized below:

Favorite Winter Sport

 Grade Snowboarding Skiing Ice Skating TOTAL 6th 68 41 46 155 7th 84 56 70 210 8th 59 74 47 180 TOTAL 211 171 163 545

Using these 545 students as the sample space, a student from this study is randomly selected.

 a.) What is the probability of selecting a student whose favorite sport is skiing? b.) What is the probability of selecting a 6th grade student? c.) If the student selected is a 7th grade student, what is the probability that the student prefers ice-skating? d.) If the student selected prefers snowboarding, what is the probability that the student is a 6th grade student? e.) If the student selected is an 8th grade student, what is the probability that the student prefers skiing or ice-skating? Answer Part a: 171/545 Part b: 155/545 = 31/109 Part c: 70/210 = 1/3 Part d: 68/211 Part e: (74 + 47)/180 = 121/180

 Topic Index | Algebra Index | Regents Exam Prep Center Created by Donna Roberts