Probability Questions ?

Question

1.Karen, Melissa, and Olivia are on the same swimming team and are each competing in the finals of the 200-meter freestyle race. There are 8 swimmers in all, and the fastest 3 swimmers win a medal. If each swimmer is equally likely to win the race, what is the probability that Karen, Melissa, and Olivia win all 3 of the medals?

2.Hiram randomly chooses a letter from the group and does not replace it. He then randomly chooses another letter. What is the probability that the first letter is an F or the second letter is a C? Assume C is not selected the first time. (Dependent Events and Not Mutually Exclusive Events) There are

4 F's

2 B's

2 D's

3 C's

2 E's

3 A's

3.Suppose you pick one coin at random, do not replace it, and then pick another coin. What is the probability that the first coin is a dime and the second coin is worth at least 5¢?(Independent and Dependent Events)

Penny: 24

Nickel: 17

Dime: 15

Quarter: 19

4.Alberto surveyed the students in his homeroom and asked if they are studying Spanish, French, both, or neither. The probability that a student is studying both Spanish and French is 0.16, the probability that a student is studying Spanish only is 0.64, and the probability that a student is studying French only is 0.4. What is the probability that a student is studying French, given that the student is studying Spanish?(Conditional Probability)

5.Sandra randomly chooses two of the shapes from the set at the same time. What is the probability that one shape is a cube or one shape is a pyramid? (Dependent Events and Not Mutually Exclusive Events)

Cube: 5

Triangle: 5

Cylinder: 5

6.Janet randomly chooses a letter from the group and does not replace it. She then randomly chooses another letter. What is the probability that the first letter is an E or the second letter is a B? Assume B is not selected the first time. (Dependent Event and Not Mutually Exclusive Events)

A: 4

B: 3

C: 2

D: 3

E: 2

F: 2

7.Janet randomly chooses a letter from the group and does not replace it. She then randomly chooses another letter. What is the probability that the first letter is an E or the second letter is a B? Assume B is not selected the first time. (Dependent Event and Not Mutually Exclusive Events)

A. 3x3x3x3x3x3

B. 3x3

C. 6x5x4

D. 6x6x6

8.Ricardo randomly chooses a block from each of the two groups shown in the figure. What is the probability that he will choose a Z from the first group and a T from the second group? (Independent and Dependent Events)

Group 1

B: 2

C:1

F: 2

K: 2

Z: 4

Group 2

Z: 1

T: 2

X: 1

M: 1

N: 2

U: 3

H: 1

9.Ricardo randomly chooses a block from each of the two groups shown in the figure. What is the probability that he will choose a Z from the first group and a T from the second group? (Independent and Dependent Events)

C: 4

E: 2

A: 2

S: 3

G: 1

O: 2

L: 1

M: 1

Which events have the same probability of occurring? Select all that apply.

A. Drawing an S or an L and then drawing an M

B. Drawing an O or an A, and then drawing an L

C. Drawing a C and then drawing a G

D. Drawing an E and then drawing an A

Answer 1

Problem (1):

You are choosing 3 from 8. The order of the 3 you have chosen doesn't matter because they will just have medals, (nothing like with first place, second place and third place).

Therefore this case is combination:

₈C₃ = 8!/(3!(8-3)!) = 56

Karen, Melissa, and Olivia winning all 3 medals is just one outcome in the 56 combinations.

Therefore:

P(Karen, Melissa and Olivia win 3 medals) =1/56