Page 159 - MAT KS3 Y8 Cambridge CheckPoint

End-of-unit review

End-of-unit review

1 If ten coins are spun together, the probability of four or more heads is 0.83.
The probability of eight or more heads is 0.05. Find the probability of:
a less than four heads b fewer than eight heads.

2 Ahmad plays chess against his father. Ahmad’s probability of winning is 0.1. His probability
of losing is 0.3.
Find the probability that:
a Ahmad will not win b Ahmad’s father will not win.

3 The letters of the word ‘EXPERIMENT’ are placed on ten separate cards. One card is chosen
at random.
a How could you make sure the card is chosen at random?
b Find the probability that the card does not show an E.
c Find the probability that the letter on the card is in the word ‘EMPIRE’.
4 A number generator produces two digits in boxes like this.
Each digit is generated randomly. It can be any digit from 0 to 9. 4 6
Find the probability that:
a the first number is 4 b the second number is less than 8 c there are no 0s.

5 Two four-sided spinners are each numbered 1 to 4.
1 1
a Construct a table to show the possible totals of the two dice. 4 2 4 2
b What is the most likely total? 3 3
c Find the probability that the total is:
i 3 ii more than 3 iii 5 or less.
d Construct a table to show the possible products when the two numbers are multiplied.
e Find the probability that the product is:
i 4 ii 11 iii more than 11 iv less than 11 v an odd number.

6 Shen wants to find the experimental probability that, when you throw three dice, all three numbers
will be the same.
a After 20 throws he has not thrown the same number three times. What is the experimental
probability of getting all three numbers the same?
b He continues to throw three dice until he has done it 200 times. Here are his results.

After 20 throws 50 throws 100 throws 200 throws
Frequency of three identical numbers 0 3 4 9

Find the experimental probability of throwing three identical numbers after 50, 100 and 200
throws.
c Explain why more throws may be necessary for Shen to be confident about the experimental
probability.
d Shen asks four friends to throw four dice 200 times. Here are their results.

Person A B C D
Frequency of three identical numbers in 200 throws 5 3 1 7
Find the experimental probability of throwing three identical numbers for each of these four people.
e Combine the results of all five people to find a new experimental probability.
f Why is the answer to part e likely to be the most reliable estimate?
15 Probability 157