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Sample Space Diagrams
2nd dice
1. Two fair dice are thrown and the scores added together. Copy and complete the sample
1st dice
space diagram showing all the outcomes.
1 2 3 4 5 6
a). i). What is the least possible score ?
1
ii). How many times does it occur ?
2
8
b). What is i). the maximum possible score, ii). the probability of
3
getting this ?
4
c). What score appears most frequently in the table?
5
d). What is the probability of this score ?
6 7
e). What is the probability of scoring an odd number?
coin
2. A die and a coin are thrown together, copy and complete this sample space.
dice
Use the diagram to find :1
2
3
4
5
6
a). the probability of a tail and a 3,
H H,1 H,1 H,1 H,1 H,1
b). the probability of a head and a 5,
T
T,6
c). the probability of a tail and a 7.
2nd dice
2nd dice
3. A tetrahedral dice (four sided) is numbered 3, 4, 5, 6. Two are thrown and the
product (multiplied) of the scores noted. Copy and complete the sample space diagram. Find
1st dice
the probability that :3 4 5 6
a). the score is greater than 8,
3
b). the score is less than 14,
4 2
c). the score is exactly 18,
5
d). the score is an odd number,
6 16 16 16 16
e). the score is a square number,
f). the score is a triangular number.
1st dice
1 2 3 4 5 6
4. Two fair dice are thrown and the difference between the dice
1
5
noted. Copy and complete the sample space diagram. What is the
2
4
probability that :3
a). there is no difference between the 2 scores,
4
b). there is a difference of 2 between the 2 scores,
5
c). there is a difference of more than 5 between the scores ?
6 5
1
1
2nd card
5. There are 5 cards numbered 1 to 5. One card is selected
at random then replaced in the pack. A second card is then
selected at random. Draw a possibility space.
Find the probability of :a). the sum of the scores is 6 or more,
b). the sum of the scores is less than 4,
c). the product of the scores is greater than 9,
d). the product of the scores is a square number,
e). the difference in the scores is exactly 3.
2
3
4
5
1st card
2
3
4
5
For these questions you will need to construct your own sample space diagrams. Look at the
questions you have already done for guidance.
6. Darby and Joan each roll a fair 6-sided dice and the number it lands on is noted. Draw out
the sample or possibility space. What is the probability that :a). they both roll a 1,
b). Joan scores exactly 4 more than Darby,
c). their number differ by exactly 3,
d). neither of them throw an even number,
e). Darby's number is bigger than Joan's number,
f). the sum of their numbers is 3 ?
7. Two unbiased dice are numbered 2, 2, 4, 4, 6, 6. They are thrown together and the
total of the two scores is found. Draw a sample space. Find the probabilities that
a). the sum is 10,
b). the sum is an odd number,
c). the sum is a square number,
d). the sum is greater than 6.
8. A coin and an ordinary die are thrown. Draw the sample space. What is the probability
a). of getting a head and a 4,
b). a tail and a prime number,
c). a head and a factor of 12,
d). a tail and a number bigger than or equal to 4 ?
*9. There are 2 bags of marbles. The first contains 2 red, 3 blue and 1 green, the second
contains 1 red, 2 blue and 1 green. A marble from each is removed, draw the sample
space. Find the probability of getting
a). 2 red, b). 2 blue, c). a red and blue, d). 2 green, e) a green and a blue