Probability Toolkit (Cambridge O Level Maths)

Sofia has a bag containing 8 blue beads and 7 red beads only.
She takes one bead out of the bag at random and replaces it.
She does this 90 times.
 
Find the number of times she expects to take a red bead.

One of the teachers at a school is chosen at random.

The probability that this teacher is female is  

There are 36 male teachers at the school.

Work out the total number of teachers at the school.

Rhiana plays a game.

The probability that she will lose the game is 0.32
The probability that she will draw the game is 0.05

Rhiana is going to play the game 200 times.

Work out an estimate for the number of times Rhiana will win the game.

The table shows the probabilities that a biased dice will land on 2, on 3, on 4, on 5 and on 6

Neymar rolls the biased dice 200 times.

Work out an estimate for the total number of times the dice will land on 1 or on 3.

A survey recorded the number of people living in each of 50 houses.
The bar chart shows the results.

One of these houses is chosen at random.

Find the probability that exactly 3 people live there.

Two houses are chosen at random from these 50 houses.
Find the probability that only one of the two houses has exactly 5 people living there.

A bag contains 7 red discs, 5 green discs and 2 pink discs.

Helen takes one disc at random, records the colour and replaces it in the bag.
She does this 140 times.
 
Find how many times she expects to take a green disc.

Helen adds 9 green discs and some pink discs to the discs already in the bag.
The probability of taking a green disc is now .
 
Find the number of pink discs that Helen added to the bag.

There are only blue counters, green counters, red counters and yellow counters in a bag.

Olga is going to take at random a counter from the bag.

The table shows the probability that Olga will take a blue counter and the probability that she will take a yellow counter.

The number of red counters in the bag is 4 times the number of green counters in the bag.

Complete the table.

There are some counters in a bag.
The counters are red or white or blue or yellow.

Bob is going to take at random a counter from the bag.

The table shows each of the probabilities that the counter will be blue or will be yellow.

There are 18 blue counters in the bag.

The probability that the counter Bob takes will be red is twice the probability that the counter will be white.

Work out the number of red counters in the bag.

A marble is going to be taken at random from a box of marbles.
The probability that the marble will be silver is 0.5

There must be an even number of marbles in the box.

Explain why.

Four friends each throw a biased coin a number of times.
The table shows the number of heads and the number of tails each friend got.

The coin is to be thrown one more time.

Which of the four friends' results will give the best estimate for the probability that the coin will land heads?
Justify your answer.

Paul says,

"With this coin you are twice as likely to get heads as to get tails."

Is Paul correct?
Justify your answer.

The coin is to be thrown twice.

Use all the results in the table to work out an estimate for the probability that the coin will land heads both times.

Becky has a biased 6-sided dice.

The table gives information about the probability that, when the dice is thrown, it will land on each number.

Number	1	2	3	4	5	6
Probability		0.18			0.26

Becky is going to throw the dice 200 times.

Work out an estimate for the number of times that the dice will land on an even number.