Conditional probability: tree diagrams

The Maths Habit Handout to print

A lottery draws 6 balls from 59.
What is the chance you match all 6?

About 1 in 45 million

Without replacement
The item is not put back, so there is one fewer next time.
Dependent
The first event changes the probability of the second.

3 red and 2 blue counters. Two are taken without replacement.

A bag has 5 red and 4 blue counters.
A red is taken and not replaced.
What is the probability that the next one is red?

48

A bag has 5 red and 4 blue counters.
A blue is taken and not replaced.
What is the probability that the next one is red?

58

A box has 6 milk and 3 dark chocolates. Sam eats two. Find the probability that they are different types.

A team has 7 girls and 5 boys. Two are picked at random to be captains. Find the probability that at least one is a girl.

A bag has 2 red and 7 blue counters. Two are taken without replacement. Find the probability of (a) two blues (b) one of each colour. (a) 4272  (b) 2872

A box has 4 lemon and 8 lime sweets. Ava eats two. Find the probability that (a) both are lime (b) they are different flavours. (a) 56132  (b) 64132

A bag has 2 red and 7 blue counters. Two are taken without replacement. Find the probability of (a) two blues (b) one of each colour. (a) 4272  (b) 2872

A bag has 5 green and 8 yellow counters. Two are taken without replacement. Find the probability of (a) two yellows (b) one of each colour. (a) 56156  (b) 80156

Conditional probability: tree diagrams worksheet, page 1

Conditional probability: tree diagrams worksheet, page 2

Answer sheet

  1. A lottery draws 3 balls from 10 without replacement. You pick 3 numbers. Find the probability that all 3 of your numbers are drawn.

    1120
  2. A bag has 3 red counters and some blue counters. Two are taken without replacement. The probability of two reds is 112. How many blue counters are there?

    6

  1. A bag has 4 red and 6 green counters. Two are taken without replacement. Find the probability that both are green.

    3090 = 13
  2. Find the probability that they are different colours.

    4890 = 815
  3. Find the probability that at least one is red.

    6090 = 23
Exit tickets to print