Question

In: Statistics and Probability

Three friends Bryce, Chris, Kate each decide to go skiing on the same day without knowing...

Three friends Bryce, Chris, Kate each decide to go skiing on the same day without knowing the other two are going as well. Bryce is going to decide between resorts A, B, P. Chris is going to decide between resorts A, S, or P. Kate is going to decide between resorts S, or A. All possible outcomes are equally likely.

1. Draw the tree diagram showing all possible outcomes for the day (the sample space).

2. What is the probability that at least two of them decide to go to the same resort?

3. What is the probability that three friends end up going to three different resorts?

Now a fourth friend, Michael, decides to go skiing on the same day as well. He is going to decide between resorts C, D, A, or S. Answer the following based on the four friends going skiing.

4. How many possible outcomes are there now? What is the probability that at least one of the four friends goes to the resort S? Hint: To avoid drawing a very large tree, you will need to use several different tools such as the multiplication rule for counting and the probability of unions of events.

Solutions

Expert Solution

Soln

There will be 3*3*2 = 18 possible outcomes

All the Possible Outcomes:

Bryce

Chris

Kate

A

A

S

A

A

A

A

S

S

A

S

A

A

P

S

A

P

A

B

A

S

B

A

A

B

S

S

B

S

A

B

P

S

B

P

A

P

A

S

P

A

A

P

S

S

P

S

A

P

P

S

P

P

A

1)

2)

Probability = Favourable Outcome (F) / Total Outcome (T)

T = 18C1 = 18

F = 11 (There are 11 combinations in which at least two of them decide to go to the same resort)

Hence,

P = 11/18 = 0.6111 or 61.11%

3)

Probability = Favourable Outcome (F) / Total Outcome (T)

T = 18C1 = 18

F = 7 (There are 7 combinations in which three friends end up going to three different resorts)

Hence,

P = 7/18 = 0.3889 or 38.89%

4)

There will be 3*3*2*4 = 72 possible outcomes

All the Possible Outcomes:

Michael

Bryce

Chris

Kate

C

A

A

S

C

A

A

A

C

A

S

S

C

A

S

A

C

A

P

S

C

A

P

A

C

B

A

S

C

B

A

A

C

B

S

S

C

B

S

A

C

B

P

S

C

B

P

A

C

P

A

S

C

P

A

A

C

P

S

S

C

P

S

A

C

P

P

S

C

P

P

A

D

A

A

S

D

A

A

A

D

A

S

S

D

A

S

A

D

A

P

S

D

A

P

A

D

B

A

S

D

B

A

A

D

B

S

S

D

B

S

A

D

B

P

S

D

B

P

A

D

P

A

S

D

P

A

A

D

P

S

S

D

P

S

A

D

P

P

S

D

P

P

A

A

A

A

S

A

A

A

A

A

A

S

S

A

A

S

A

A

A

P

S

A

A

P

A

A

B

A

S

A

B

A

A

A

B

S

S

A

B

S

A

A

B

P

S

A

B

P

A

A

P

A

S

A

P

A

A

A

P

S

S

A

P

S

A

A

P

P

S

A

P

P

A

S

A

A

S

S

A

A

A

S

A

S

S

S

A

S

A

S

A

P

S

S

A

P

A

S
orchestra answered 1 year ago
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