Answer:
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)
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)
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
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:
Therefore 0.3125 is the required probability here
This is a simple differentiation problem. Let's start by taking the derivative of both sides (with respect to x):
Simplify:
Solve for dy/dx:
Now, plug in the given points:
Further simplification gives:
So,
your answer is 11/23 or
B.
