Question

 

1. Using basic properties of probabilities, state two reasons how you know this information is not accurate.

Client Type	Corporate	Small Business	Legal	Government	Private
Probability	0.45	0.11	-0.09	0.29	0.7

2. The next interviewer you meet with is excited to show you a dice game he has developed that he is hoping to sell to a local casino. The game involves using two 10 sided dice with faces numbered 1 through 10.

Create a table to show all outcomes of one roll of the dice.

 

3. Using the same scenario as in number 2, determine the probability of rolling a sum of 11 on the two dice.

4. Using the same scenario as in number 2, determine the probability of rolling at least one 7 on the two dice.

5. Using the same scenario as in number 2, determine the probability of rolling doubles twice in a row.

6. Using the same scenario as in number 2, your interviewer tells you that the game costs $1 to play and it has an expected value of 47 cents for every dollar spent. Use the following payouts to determine the expected value of the game. Do you agree with your co-worker’s assertion?

Roll	Sum of 19	Sum of 17	Sum of 15	Sum of 13	Doubles	Other
Winnings	$5	$3	$2	$1	$.5	$0

Answer 1

1. First basic reason is that we can't have probability to be negative which is the case here for legal business. Second basic reason is that the sum of probabilities is greater than 1 which is not possible as these are disjoint events as they are different types of events.

2.

3. The number or possibilities for getting a sum of 11 are (1,10) (10,1) (2,9) (9,2) (3,8) (8,3) (4,7) (7,4) (5,6) (6,5)

So there are 10 possible events each with equal probabilities of 1/36

So the probability of getting a sum of 11 is 10/36

4.

The number or possibilities for getting at least one 7 on the two dice are (7,1) (7,2) (7,3) (7,4) (7,5) (7,6) (7,7) (7,8) (7,9) (7,10) (1,7) (2,7) (3,7) (4,7) (5,7) (6,7) (8,7) (9,7) (10,7)

So there are 19 possibilities each with probability 1/36

So the required probability is 19/36