A candy jar contains the following candies: 7 cherry, 3 lemon, 4 lime, 6 orange. TWO (2) candies are drawn WITH REPLACEMENT. Use this information to answer questions #1 - 3.1) P(BOTH orange) =1 pointYour answer2) P(cherry AND lime) =1 pointYour answer3) P(lemon on the 2nd draw GIVEN THAT the first draw was orange) =1 pointYour answer
Question
A candy jar contains the following candies: 7 cherry, 3 lemon, 4 lime, 6 orange. TWO (2) candies are drawn WITH REPLACEMENT. Use this information to answer questions #1 - 3.1) P(BOTH orange) =1 pointYour answer2) P(cherry AND lime) =1 pointYour answer3) P(lemon on the 2nd draw GIVEN THAT the first draw was orange) =1 pointYour answer
Solution
Sure, let's solve these step by step.
First, let's determine the total number of candies in the jar:
- Cherry: 7
- Lemon: 3
- Lime: 4
- Orange: 6
Total candies = 7 + 3 + 4 + 6 = 20
- P(BOTH orange): Since the candies are drawn with replacement, the probability of drawing an orange candy each time remains the same.
P(orange on first draw) = Number of orange candies / Total number of candies = 6/20 = 3/10
Since the draws are independent (with replacement), the probability of drawing an orange candy on both draws is: P(BOTH orange) = P(orange on first draw) * P(orange on second draw) = (3/10) * (3/10) = 9/100
- P(cherry AND lime): Again, since the candies are drawn with replacement, the probability of each draw remains the same.
P(cherry on first draw) = Number of cherry candies / Total number of candies = 7/20 P(lime on second draw) = Number of lime candies / Total number of candies = 4/20 = 1/5
Since the draws are independent: P(cherry AND lime) = P(cherry on first draw) * P(lime on second draw) = (7/20) * (1/5) = 7/100
- P(lemon on the 2nd draw GIVEN THAT the first draw was orange): Since the draws are with replacement, the probability of drawing a lemon on the second draw is not affected by the first draw.
P(lemon on second draw) = Number of lemon candies / Total number of candies = 3/20
Therefore, P(lemon on the 2nd draw GIVEN THAT the first draw was orange) = 3/20
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