A spinner has a red section, a blue section, and a green section. When the spinner is spun twice, the probability that it will land on red both times
is 0.16. What is the probability that, when the spinner is spun twice, both of the two spins
land on either green or blue?
When we want to find the probability of two events occurring, we multiply their
relevant probabilities together. In this case, we’re told that the probability that the spinner will land on red twice
— that’s red and red again — is 0.16. That means the probability of getting two reds is 0.16. But we can also write it as the probability of red multiplied by the probability of
red or the probability of red squared.
Since the probability of getting red squared is equal to 0.16, we can square root
both sides of the equation to get the probability of red is 0.4. Now, this helps us since we’re trying to find the probability that the spinner lands
on green or blue during both spins. This means it cannot land on red during either spin.
Since the probability it lands on red is 0.4 and the sum of the probabilities of all
outcomes is one, we can find the probability it lands on green or blue by
subtracting 0.4 from one. One minus 0.4 is 0.6. So the probability the spinner lands on green or blue during one spin is 0.6.
We said that the probability of two events occurring is found by multiplying their
probabilities together. So the probability the spinner lands on green or blue during the first spin and then
on green or blue during the second spin is 0.6 multiplied by 0.6. Six times six is 36. Since 0.6 is 10 times smaller than six, our answer will be 10 times and then another
10 times smaller than 36.
Another way of saying that is that it will be 100 times smaller. 36 divided by 100 is 0.36. So the probability the spinner lands on green or blue during both spins is 0.36.