In part a, we want to find the probability that Matt takes a red counter out of the bag.
To do this, we use the ratio for the probability of an event which is shown below.
P(event) = number of favorable outcomes/total number of outcomes
Since there are 6 red counters in the bag, the number of favorable outcomes is 6 and since there are 18 counters in all and it’s equally likely that we will choose any of the counters, the total number of outcomes is 18.
Therefore, the probability that Matt chooses a red counter is 6/18 which reduces to 1/3.
In part b, we start off with our ratio again for the probability of an event.
Number of favorable outcomes
/total number of outcomes
Since there are 14 counters in the bag that aren’t blue, the number of favorable outcomes is 14.
Since there are 18 cubes in all, the total number of outcomes is 18.
So we have 14/18.
This reduces to 7/9.
So the probability of choosing a counter that isn’t blue is 7/9.