It’s Louie’s last day in school before the summer holidays. His teacher has asked the children to help tidy up the classroom.
Louie finds a bag of counters in a toy box. There are 9 counters in the bag.
7 of the counters are yellow.
2 of the counters are green.
Louie takes at random two counters from the bag.
Can you work out the probability that Louie takes one counter of each colour.
Answer:
There are two possibilities of picking one counter of each colour.
Either pick the green counter first and then the yellow or a yellow counter followed by a green.
We need to calculate the probability of both of these scenarios and then add the two together.
Probability of picking a green counter followed by a yellow counter:
There are nine counters in the bag and two of them are green, then there are eight counters in the bag and seven of them are yellow.
2/9 x 7/8 = 14/72
Probability of picking a yellow counter followed by a green counter:
There are nine counters in the bag and seven of them are yellow, then there are eight counters in the bag and two of them are green.
7/9 x 2/8 = 14/72
To find out the probability of picking one of each colour, we must add the probabilities of the two scenarios together:
14/72 + 14/72 = 28/72
Answer = 28/72 or 7/18 in its simplest form