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16.2 Sample space diagrams

) Exercise 16.2

1 Xavier throws a coin and a six-sided dice at the same time.
a Draw a sample space diagram to show all the possible outcomes.
b On your diagram, circle points that show a tail and an odd number.
c Work out the probability of his scoring:
i an odd number ii a tail and an odd number iii not a tail and not an odd number.

2 This is a sample space diagram for two dice thrown at the same time. 6 + + + + + +
Work out the probability of both dice showing: 5 + + + + + +
a 5 or more b 4 or more c 3 or more. 4 + + + + + +

3 + + + + + +
3 Draw a probability space diagram for two dice being thrown together. 2 + + + + + +
Use your diagram to find the probability of scoring:
a two odd numbers b two even numbers 1 + + + + + +
c one odd number and one even number.
1 2 3 4 5 6
4 This is the sample space diagram for the scores on two spinners. 3 + + + + +
a Write down the numbers on each spinner. 2 + + + + +
b Both spinners are fair. Find the probability of scoring:
i two odd numbers ii at least one 3 iii 2 or less on both spinners. 1 + + + + +

5 a Draw a sample space diagram for these two spinners. 1 2 3 4 5
b Find the probability of scoring:
i two even numbers ii two odd numbers 3 1 6 2
iii a total of 5 iv a total of more than 5.
2 4
6 There are four girls and three boys in a group. Their names are shown
in the sample space diagram. One girl and one boy are chosen at random.
Find the probability that: Shen + + + +
a Maha is not chosen b Shen is not chosen. Jake + + + +
c neither Maha nor Shen is chosen.
Razi + + + +
7 A computer chooses two random digits. Each digit can
be 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9. Maha Sasha Oditi
a Show the possible choices on a sample space diagram. Harsha
b Find the probability that:
i both digits are 7 ii at least one digit is 7 iii neither digit is 7 iv both digits are odd.
8 Anders throws a 10-faced dice with numbers from 1 to 10. Then he spins a coin.
a Draw a sample space diagram to show all the possible outcomes.
b Find the probability of scoring: i a head and a multiple of 3 ii a tail and a prime number.
9 Tanesha chooses one letter at random from the word DEAR.
Dakarai chooses one letter at random from the word ROAD.
a Draw a sample space diagram to show all the possible outcomes.
b Find the probability that:
i both choose R ii at least one chooses R
iii both choose the same letter iv they each choose different letters.

154 16 Probability