Probability

A bistro menu has 5 starters, 8 main courses and 4 desserts.

Callum chooses one starter, one main course and one dessert.

Work out the number of different three-course meals Callum can choose.

A bag contains 4 green counters, 7 yellow counters and 9 white counters.

A counter is taken from the bag at random.

Find the probability that the counter is not green.

A spinner can land on red, blue or green only.

P(red) = 0.3 and P(blue) = 0.25.

1. Work out the probability that the spinner lands on red or blue.
2. Work out the probability that the spinner lands on green.

Two fair spinners are each numbered 1, 2, 3 and 4.

Both spinners are spun and the two scores are added together.

1. Complete the sample space diagram.
2. Work out the probability that the total is 5
3. Work out the probability that the total is greater than 6

Twelve cards are numbered 1 to 12. One card is taken at random.

Event A: the number is even.
Event B: the number is a multiple of 5
Event C: the number is an odd prime number.

1. Write down two of the events that are mutually exclusive. Give a reason for your answer.
2. Work out the probability that the number is even or an odd prime number.
3. Leah says, "P(A or B) = P(A) + P(B)". Explain why Leah is wrong.

A four-sided spinner can land on 1, 2, 3 or 4.

The table shows some of the probabilities.

1. Work out the probability that the spinner lands on 4.
2. The spinner is spun 200 times. Work out an estimate for the number of times it lands on 4.

Zainab and Theo play a game with two fair six-sided dice.

They roll both dice and multiply the two scores.
Zainab wins if the answer is even.
Theo wins if the answer is odd.

1. Show that the game is not fair.
2. They play the game 60 times. Work out the number of games Theo should expect to win.
3. Theo actually wins 18 of the 60 games. Kemi says, "The dice must be biased." Is Kemi right? Give a reason for your answer.

80 adults went to a gym on Saturday.

45 of the adults went to a morning class. The rest went to an afternoon class.

Of the adults at the morning class, 30 did yoga.

Of the adults at the afternoon class, 12 did yoga.

1. Complete the frequency tree.
2. One of the 80 adults is chosen at random. Find the probability that this adult went to the morning class and did yoga.

A running club has 120 members. Each member is an adult or a junior.

70 of the members are adults. The rest are juniors.

25 of the adults ran a marathon last year.

11 of the juniors ran a marathon last year.

1. Work out the number of juniors in the club.
2. Work out the number of adults who ran a marathon last year.
3. One of the members who ran a marathon last year is chosen at random. Work out the probability that this member is a junior.

The passcode for a tablet is a 4 digit number.

The first digit cannot be 0.

Digits may repeat.

1. Work out the number of different passcodes that are possible.
2. Ruby does not know the passcode. She types one 4 digit number at random, with a non-zero first digit. Write down the probability that Ruby types the correct passcode.

A bag contains 3 red counters and 7 blue counters.

Kira takes a counter at random, notes its colour and puts it back.

She then takes a second counter at random.

1. Complete the probability tree diagram for the two picks.
2. Work out the probability that both counters are blue.

A box contains 5 red pens and 4 blue pens.

Milo takes a pen at random and does not replace it.

He then takes a second pen at random.

1. Complete the probability tree diagram.
2. Work out the probability that Milo takes at least one red pen.