Probability (higher) Flashcards
Marie made a 5-sided spinner. She used it to play a board game with her friend. They thought the spinner wasn’t very fair as it seemed to land on some numbers more than others. They spun the spinner 200 times and the results are shown in the table.
a) Work out the experimental probability of each number.
b) How many times would you expect each number to occur if the spinner is fair?
c) Do you think that the spinner is fair? Give a reason for your answer.
a) See table
b) 40 (200÷5)
c) No, it is weighted towards the side with numbers 4 and 5 as they come up much more often than you would expect.
A sampling bottle contains 20 balls. The balls are either black or white. Kenny conducts an experiment to see how many black balls are in the bottle. He takes various numbers of samples and records how many of them showed a black ball. The results are shown in the table.
a) Calculate the experimental probability of getting a black ball at each stage.
b) Using this information, how many black balls do you think are in the bottle?
a) See table
b) 8 (1987÷5000×8)
Note: use the probability from the largest sample as that will be the most reliable.
A four-sided dice has faces number 1, 2, 3 and 4. Five pupils throw the dice to see if it biased. They each throw it a different number of times and their results are shown in the table.
a) Which pupil will have the most reliable set of results and why?
b) Add up all the score columns and work our the relative frequency of each score. Give your answer to 2 decimal places.
c) Is the dice biased? Explain your answer.
a) Caryl, because she repeated the experiment the most number of times.
b) See table.
c) Yes. Sides 1 and 2 come up more than twice as often as sides 3 and 4.
Choosing a card at random from a pack of yellow cards number 1 to 10. Complete each of these sentences with either: “impossible”, “not likely”, “50-50 chance”, “quite likely”, or “certain”.
The likelihood that the next card chosen will be…
a) a four is…
b) pink is…
c) seven is…
d) a number less than 11 is…
e) a number bigger than 11 is…
f) an even number is…
g) a number more than 5 is…
h) a multiple of 1 is…
i) a prime number is…
The likelihood that the next card chosen will be…
a) a four is…not likely
b) pink is…impossible
c) seven is…not likely
d) a number less than 11 is…certain
e) a number bigger than 11 is…impossible
f) an even number is…50-50 chance
g) a number more than 5 is…50-50 chance
h) a multiple of 1 is…certain
i) a prime number is…quite likely
Jane has two 4-sided spinners. One has the numbers 1 to 4 and the other has the numbers 5 to 8.
The table shows all the ways the spinner can land. Some of the total scores are filled in.
a) Complete the table to show all the possible scores.
b) How many of the total scores are 9?
c) What is the probability of the total score being 9?
a) See table
b) 4
c) 4÷16 = 0.25
The table shows information about the number of items in Gemma’s music collection.
a) How many pop tapes does she have?
b) How many items of folk music does she have?
c) How many CDs does she have?
d) If a CD is chosen at random from all the CDs, what is the probability that it will be a pop CD?
a) 16
b) 16
c) 73
d) 51÷73= 0.70 (2dp)
The two-way table shows the wages for the men and women in a factory.
a) What percentage of the men earn between £250 and £300 per week?
b) What percentage of the women each between £250 and £300 per week?
c) Is it possible to work out the mean wage of the men and women?
a) 48 ÷ 120 = 40%
b) 27 ÷ 60 = 45%
c) No, as you don’t know how much the people who get over £350 actually earn.
