Answer: 0.47
Step-by-step explanation:
The probability that Matt does not get any red counters is equal to the probability that in both random selections, Matt gets a green counter.
For the first selection, we have a total of 10 counters, 3 red and 7 green, then the probability of getting a green one is:
p = 7/10.
For the second selection, we have 9 counters, 3 red and 6 green (because one green is already taken)
then the probability of getting a green one is:
p = 6/9
And the joint probability of both events is equal to the product of the probability of each event, this is:
p = (7/10)*(6/9) = 42/90 = 0.47
