Bowl #1 contains 4 grape candies, 5 lemon candies, 6 cherry candies and 5 raspberry candies.
Bowl #2 contains 8 grape candies, 5 lemon candies, 4 cherry candies and 3 raspberry candies.
(c) What is the probability that the two selected candies are the same flavour?
(d) What is the probability that the two selected candies are different colours?
(e) What is the probability that the first selected candy is lemon or that the second selected candy is cherry?
Am I to assume one candy is selected at random from each bowl?
If so, then c) Pr=4/20*8/20
d) pr=1-pr(same)=1=4/20*8/20-5/20*5/20 - 6/20*4/20-5/20*3/20
e. pr=5/20*4/20
yes but how are you getting e?
P(Lemon)+P(Cherry)-P(Lemon n Cherry)
is a formula that was given earlier today just don't quite understand.
To find the probability for each scenario, we need to first determine the total number of candy combinations and then the number of desired outcomes for each scenario.
(a) To find the total number of candy combinations, we need to calculate the total number of candies in each bowl and consider all possible selections.
Total candies in Bowl #1: 4 + 5 + 6 + 5 = 20
Total candies in Bowl #2: 8 + 5 + 4 + 3 = 20
The total number of candy combinations can be found by multiplying the number of candies in Bowl #1 by the number of candies in Bowl #2.
Total candy combinations = 20 * 20 = 400
Now, let's calculate the desired outcome for each scenario:
(c) What is the probability that the two selected candies are the same flavor?
For the candies to be the same flavor, we need to select two candies of the same flavor from either bowl. We can calculate this by summing the products of the number of each type of candy in Bowl #1 and the number of the same type of candy in Bowl #2.
Total same flavor combinations = (4 * 8) + (5 * 5) + (6 * 4) + (5 * 3) = 32 + 25 + 24 + 15 = 96
Probability = Total same flavor combinations / Total candy combinations
Probability = 96 / 400
Probability = 0.24
Therefore, the probability that the two selected candies are the same flavor is 0.24.
(d) What is the probability that the two selected candies are different colors?
For the candies to be different colors, we need to select one candy of any flavor from Bowl #1 and one candy of any flavor from Bowl #2. We can calculate this by multiplying the total number of candies in Bowl #1 by the total number of candies in Bowl #2.
Total different color combinations = Total candies in Bowl #1 * Total candies in Bowl #2
Total different color combinations = 20 * 20 = 400
Probability = Total different color combinations / Total candy combinations
Probability = 400 / 400
Probability = 1
Therefore, the probability that the two selected candies are different colors is 1.
(e) What is the probability that the first selected candy is lemon or the second selected candy is cherry?
To find the number of desired outcomes for this scenario, we need to sum the products of the number of lemon candies in Bowl #1 and the total number of candies in Bowl #2, and the products of the total number of candies in Bowl #1 and the number of cherry candies in Bowl #2.
Total desired outcomes = (5 * 20) + (20 * 4) = 100 + 80 = 180
Probability = Total desired outcomes / Total candy combinations
Probability = 180 / 400
Probability = 0.45
Therefore, the probability that the first selected candy is lemon or the second selected candy is cherry is 0.45.