Question

Matt has a bag with 3 red counters and 7 green counters. Matt picks a counter at random, and then picks another counter. Using the tree diagram drawn above, work out the probability that Matt does not get any red counters.

Answer 1

Answer: 0.47

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