Page 157 - MAT KS3 Y8 Cambridge CheckPoint

15.4 Experimental and theoretical probabilities

✦ Exercise 15.4

1 Alicia has a biased coin (it has been altered to land on one side more often). She wants to find the
experimental probability of getting a head.
She spins the coin 10 times. She gets 6 heads and 4 tails.
a What is the experimental probability of getting a head based on these 10 throws? Give your
answer as a decimal.
b Explain why this is not a reliable estimate of the probability.
She spins the coin another 10 times. This time she gets 3 heads and 7 tails.
c Find the experimental probability of getting a head based on the 20 throws so far.
She spins the coin another 30 times and gets 9 heads and 21 tails.
d Find the experimental probability of getting a head based on all the throws so far.
Another 50 throws give 19 heads and 31 tails.
e Find the experimental probability of getting a head based on all the throws so far.
f Explain why the last estimate of the probability of getting a head is the most reliable one.
2 Zalika throws four dice at the same time.
a What is the smallest possible total? b What is the largest possible total?
Zalika wants to find the
experimental probability of Throws of four dice 25 50 100 150 200
scoring a total of 15 or more when Frequency of a total of 15 or more 7 16 42 68 88
she throws four dice. She decides
to do a simulation on a spreadsheet. Her results are in the table above.
c Find separate estimates of the probability of a total of 15 or more based on 25 throws, 50 throws,
100 throws, 150 throws and 200 throws.
Mia repeats Zalika’s experiment
and gets these results. Throws of four dice 25 50 100 150 200
d Find Mia’s successive estimates Frequency of a total of 15 or more 11 24 45 76 94
of the probability.
e Compare Zalika’s results and Mia’s results.
f Put Zalika’s and Mia’s results together to get an experimental probability based
on all 400 results.
3 Maha spins a coin 10 times. She gets 8 heads and 2 tails.
a Find the experimental probability of throwing: i a head ii a tail.
b Is there evidence that Maha is not throwing the coin fairly?
Hassan spins a coin 100 times. He gets 80 heads and 20 tails.
c Find the experimental probability of throwing: i a head ii a tail
d Is there evidence that Hassan is not throwing the coin fairly?
4 Oditi makes a dice out of card. She tests it by throwing
it 30 times. She gets these results. Score 1 2 3 4 5 6
a Read what Oditi says. Is she correct? Give a reason for Frequency 4 4 5 4 9 4
your answer.

The dice is biased because 5 appeared much
more than the other numbers.

15 Probability 155