Question

You have 2 fair six-sided dice: one that is red and one that is blue. You conduct a random experiment by rolling the red die first and then rolling the blue die. Use this information and answer questions 2a to 2e.

2a) Determine whether following statements are outcome or event.
You roll a red 1 and blue 3.
You roll a red 2 and blue 5.
The sum of two dice is greater than 9.  

2b)  How many outcomes are there in the sample space? (Use integer)

2c)  What is the probability that you roll a red 3 and blue 4? (use 4 decimal places)

2d)  What is the probability that the sum of your roll is 7? (use 3 decimal places)

2e)  What is the probability that the sum of your roll is 8? (3 decimal places)

Answer 1

(2a)

(i) You roll a Red 1 and Blue 2: Outcome

(ii) You roll a Red 2 and Blue 5: Outcome

(iii) The sum of two dice is greater than 9: Event

(2b) Total number of outcomes in the Sample Space: 6 X 6 = 36

(2c) P(Red = 3, Blue = 4) = 1/36 = 0.0278

(2d) P(Sum = 7) :

Favorable events:
(Red =1, Blue = 6), (Red = 2, Blue = 5), (Red= 3, Blue = 4), (Red = 4, Blue = 3), (Red = 5, Blue = 2), (Red = 6, Blue = 1): 6 Nos.

So,

P(sum is 7) = 6/36 = 0.167

(2e) P(Sum = 8):

Favorable Events:
(Red = 2, Blue = 6), (Red = 3, Blue = 5), (Red = 4, Blue = 4), (Red = 5, Blue = 3), (Red = 6, Blue = 2): 5 Nos.

So,

P(Sum = 8) = 5/36 = 0.139