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Question : A bag contains 6 cherry 3 orange and 2 lemon candies : 2151697

**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

**A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability.**

1) All cherry

A) 0.7272

B) 0.3636

C) 0.1091

D) 0.1212

2) All orange

A) 0.0011

B) 0.0182

C) 0.0061

D) 0.7272

3) All lemon

A) 0.1212

B) 0.061

C) 1

D) 0

4) 2 cherry, 1 lemon

A) 0.7272

B) 0.1212

C) 0.1818

D) 0.3636

5) One of each flavor

A) 0.3636

B) 0.1818

C) 0.2182

D) 0.0667

6) 2 orange, 1 lemon

A) 0.0303

B) 0.3636

C) 0.0364

D) 0.1091

7) 1 cherry, 2 lemon

A) 0.0303

B) 0.0424

C) 0.3636

D) 0.0364

**Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.**

8) A royal flush (5 highest cards of a single suit) in poker

A) 2.75 × 10^{-4}

B) 1.98 × 10^{-3}

C) 1.54 × 10^{-6}

D) 3.85 × 10^{-7}

9) In poker, a flush (5 in same suit) in any suit

A) 0.00198

B) 0.000347

C) 0.00122

D) 0.000495

10) In poker, a full house (3 cards of one value, 2 of another value)

A) 3.85 × 10^{-5}

B) 6.55 × 10^{-3}

C) 9.20 × 10^{-6}

D) 1.44 × 10^{-3}

11) In poker, four of a kind (4 cards of the same value)

A) 1.85 × 10^{-5}

B) 2.00 × 10^{-5}

C) 4.34 × 10^{-4}

D) 2.40 × 10^{-4}

12) In poker, a straight flush (5 in a row in a single suit, but not a royal flush)

A) 1.39 × 10^{-5}

B) 9.23 × 10^{-6}

C) 2.31 × 10^{-6}

D) 1.23 × 10^{-5}

13) In bridge, 6 of one suit, 4 of another, and 3 of another

A) 0.0022

B) 0.0060

C) 0.0133

D) 0.00055

14) In bridge, all cards in one suit

A) 3.14 × 10^{-11}

B) 1.57 × 10^{-12}

C) 6.30 × 10^{-12}

D) 3.14 × 10^{-12}

15) In bridge, 4 aces

A) 0.00118

B) 0.01056

C) 0.00264

D) 0.00059

16) In bridge, exactly 3 kings and exactly 3 queens

A) 0.00024

B) 0.00097

C) 0.00337

D) 0.00018

**Solve.**

17) A 6-sided die is rolled. What is the probability of rolling a number less than 6?

A) 5/7

B) 1/6

C) 5/6

D) 1/3

18) Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 3?

A) 2

B) 1/2

C) 17/18

D) 1/18

19) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10?

A) 1/12

B) 3

C) 5/18

D) 1/18

20) A lottery game contains 26 balls numbered 1 through 26. What is the probability of choosing a ball numbered 27?

A) 1/26

B) 26

C) 1

D) 0

21) In a state lotto you have to pick 4 numbers from 1 to 46. If your numbers match those that the state draws, you win. If you buy 3 tickets, what is your probability of winning?

A) 1/163185

B) 8/489555

C) 1/54395

D) 7/489555

**Solve the problem.**

22) Estimate the probability that at least 2 of the 50 state governors have the same birthday.

A) 0.956

B) 0.965

C) 0.970

D) 0.950

23) What is the probability that at least 2 of the 435 members of the House of Representatives have the same birthday?

A) 0.996

B) 0.995

C) 0.999

D) 1

24) What is the probability that at least 2 students in a class of 36 have the same birthday?

A) 0.849

B) 0.832

C) 0.814

D) 0.799

25) An elevator has 4 passengers and 8 floors. Find the probability that no 2 passengers get off on the same floor considering that it is equally likely that a person will get off at any floor.

A) 0.410

B) 0.500

C) 0.610

D) 0.910

26) At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5 people from town C. If the council consists of 5 people, find the probability of 3 from town A and 2 from town B.

A) 0.072

B) 0.036

C) 0.023

D) 0.076

27) At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5 people from town C. If the council consists of 5 people, find the probability of 2 from town A, 2 from town B, and 1 from town C.

A) 0.076

B) 0.038

C) 0.090

D) 0.189

28) Suppose 6 people sit at a circular table. Find the probability that 2 particular people are sitting next to each other.

A) 0.2

B) 0.4

C) 0.1

D) 0.33

29) A ring contains 8 keys: 1 red, 1 blue, and 6 gold. If the keys are arranged at random on the ring, find the probability that the red is next to the blue.

A) 0.047

B) 0.143

C) 0.286

D) 0.25

30) A roulette wheel contains 24 slots numbered 1 through 24. The odd number slots are colored purple and even number slots are colored blue. When the wheel is spun, a ball rolls around the rim and falls into a slot. What is the probability that the ball falls into an even number slot?

A) 0.6

B) 0.52

C) 0.5

D) 0.45

31) A roulette wheel contains 84 slots numbered 1 through 84. The slots 1,4,7,¼ are red, the slots 2,5,8, ¼ are green, and the slots 3, 6, 9,.... are brown. When the wheel is spun, a ball rolls around the rim and falls into a slot. What is the probability that the ball falls into a green slot?

A) 2/5

B) 2/3

C) 1/4

D) 1/3