Little_Louis
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- Mar 26, 2022
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Question: Two fair sided dice with numbers 1 to 6 on the sides are thrown and the two numbers uppermost noted. The events X, Y and Z are defined as follows
X = the total of the two numbers is even
Y = the maximum of the two numbers is less than 5
Z = the total of the two numbers is greater than 9
Which one of the following statements is always correct?
Plot the sample space for two dice.
X - the total number of evens in the sample space is 18 pairs = 18/36 = probability of 0.5
Y - the largest of the two numbers is less than 5 - so there are 16 pairs, so I think this is 16/36 = probability of 0.44 (2dp)
Z - the total of two numbers is greater than 9 - so there are pairs, 6/36 = probability 0.17
I think out of the 4 statements, no 3 is the correct option. Please could someone confirm I have approached/completed this correctly. Many thanks.
X = the total of the two numbers is even
Y = the maximum of the two numbers is less than 5
Z = the total of the two numbers is greater than 9
Which one of the following statements is always correct?
- The probability of X is less than that of Y
- The probability of Z is 0.25
- If Z occurs then the probability of X also occurring is greater than it would otherwise be
- The probability that both X and Y occur is greater than 0.25
Plot the sample space for two dice.
1 | 2 | 3 | 4 | 5 | 6 | |
1 | (1, 1) | (1, 2) | (1, 3) | (1, 4) | (1, 5) | (1, 6) |
2 | (2, 1) | (2, 2) | (2, 3) | (2, 4) | (2, 5) | (2, 6) |
3 | (3, 1) | (3, 2) | (3, 3) | (3, 4) | (3, 5) | (3, 6) |
4 | (4, 1) | (4, 2) | (4, 3) | (4, 4) | (4, 5) | (4, 6) |
5 | (5, 1) | (5, 2) | (5, 3) | (5, 4) | (5, 5) | (5, 6) |
6 | (6, 1) | (6, 2) | (6, 3) | (6, 4) | (6, 5) | (6, 6) |
X - the total number of evens in the sample space is 18 pairs = 18/36 = probability of 0.5
Y - the largest of the two numbers is less than 5 - so there are 16 pairs, so I think this is 16/36 = probability of 0.44 (2dp)
Z - the total of two numbers is greater than 9 - so there are pairs, 6/36 = probability 0.17
- The probability of X is less than that of Y (0.5 > 0.44 (2dp) FALSE
- The probability of Z is 0.25 (Z = 0.17) FALSE
- If Z occurs then the probability of X also occurring is greater than it would otherwise be (Z + X/Z) = (0.25 + 0.5)/0.25 = 3 TRUE
- The probability that both X and Y occur is greater than 0.25 (0.5 x 0.44 = 0.22) FALSE
I think out of the 4 statements, no 3 is the correct option. Please could someone confirm I have approached/completed this correctly. Many thanks.