You have a bag full of apples. There are 8 Jonathan (red), 4 Granny Smith (green), and 5 Golden Delicious (yellow) apples in the bag. The apples are all of similar size and shape. You reach into the bag (without looking) and pull out the number of apples listed in each scenario below.

a) Select 3 apples with replacement. Find the probability that all three are green.

b) Select 3 apples with replacement. Find the probability that none are red.

c) Select 4 apples without replacement. Find the probability that you get at LEAST 2 red apples.

d) Select 2 apples without replacement. Find the probability that the second apple is yellow given that the first apple is red.

Question

Gilberto Boyle

Mathematics

12 January, 09:03

You have a bag full of apples. There are 8 Jonathan (red), 4 Granny Smith (green), and 5 Golden Delicious (yellow) apples in the bag. The apples are all of similar size and shape. You reach into the bag (without looking) and pull out the number of apples listed in each scenario below.

a) Select 3 apples with replacement. Find the probability that all three are green.

b) Select 3 apples with replacement. Find the probability that none are red.

c) Select 4 apples without replacement. Find the probability that you get at LEAST 2 red apples.

d) Select 2 apples without replacement. Find the probability that the second apple is yellow given that the first apple is red.

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Answers (1)

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Quinn Vaughan · Answer 1

Step-by-step explanation:

There are 8 Jonathan (red), 4 Granny Smith (green), and 5 Golden Delicious (yellow) apples in the bag.

a) Select 3 apples with replacement. Find the probability that all there are green.

Given that we are taking all apples with replacement, the probability of getting a green apples remains the same in all 3 trials. Therefore the probability here is computed as:

= (Number of green apples/Total apples) = (4/17) ^3 = 0.0130

Therefore 0.0130 is the required probability here.

b) Select 3 apples with replacement. Find the probability that none are red

Probability that none are red is computed here as:

= (Number of non red apples/Total apples) = (9/17) ^3 = 0.14838

Therefore 0.14838 is the required probability here

c) Select 4 apples with replacement. Find the probability that you get at least 2 red apples

Probability that we get at least 2 red apples when 4 apples are drawn is computed here as: = 1 - (Probability that no red apple is taken out when 4 apples are taken out + Probability that 1 red apple is taken out when 4 apples are taken out) = 1 - 8C0 x 9C4 + 8C1 x 9C3 / 17C4 = 1 - 0.3353 = 0.6647

Therefore 0.6647 is the required probability here

d) Select 2 apples with replacement. Find the probability that the second apple is yellow given that the first apple is red.

Given that the first apple is red, we are left with 16 apples out of which 5 are yellow. Therefore the required probability here is computed as: = 5/16 = 0.3125

Therefore 0.3125 is the required probability here