A box contains twelve candies, five reds, four greens, and three blues. You select one piece at random, then replace it, then you select another. If
P(BG) is the probability of selecting a blue first and a green second, find the following probabilities.
a. P(RG)=
b. P(BB)=
c. P(GB)=
d. P(not RR)=
The important difference between this question and your previous one is that you are replacing the candy after you picked it.
you have 5 R's , 4 G's, and 3 B's for a total of 12
so Prob(BG) = (3/12)(4/12) = (1/4)(1/3) = 1/12
How does this calculation differ from our calculation in your previous post?
Do the rest in the same way.
To find the probabilities, we need to first determine the total number of candies in the box and the number of candies of each color. Let's start by counting:
Total number of candies = 12
Number of red candies = 5
Number of green candies = 4
Number of blue candies = 3
Since the candies are replaced after each selection, the probability of selecting a particular color remains the same for each selection.
a. P(RG) is the probability of selecting a red candy first and a green candy second. We can find this by multiplying the individual probabilities.
P(R) = Number of red candies / Total number of candies = 5/12
P(G) = Number of green candies / Total number of candies = 4/12
P(RG) = P(R) * P(G) = (5/12) * (4/12) = 20/144 = 5/36
b. P(BB) is the probability of selecting a blue candy first and a blue candy second. Again, we multiply the individual probabilities.
P(B) = Number of blue candies / Total number of candies = 3/12
P(BB) = P(B) * P(B) = (3/12) * (3/12) = 9/144 = 1/16
c. P(GB) is the probability of selecting a green candy first and a blue candy second.
P(GB) = P(G) * P(B) = (4/12) * (3/12) = 12/144 = 1/12
d. P(not RR) is the probability of not selecting a red candy in both selections. We can find this by subtracting the probability of selecting a red candy in both selections from 1.
P(not RR) = 1 - P(RR)
For the first selection, the probability of not selecting a red candy is (total number of candies - number of red candies) / total number of candies = 7/12.
Since the candies are replaced after the first selection, the probability of not selecting a red candy in the second selection is also 7/12.
P(not RR) = (7/12) * (7/12) = 49/144