A batch consists of 20 bad apples and 80 good ones. What is the probability of selecting 2 good apples when two are randomly selected if the first selection is replaced before the second is made?
With replacement, the probability of selecting a good apple stays at 60/80=3/4.
For a two-step experiment, the probability is the product of individual steps, hence, probability of select a good apple in each pick is
(3/4)^2=9/16
To calculate the probability of selecting 2 good apples when two are randomly selected with replacement, we need to first determine the probability of selecting a good apple on each individual selection.
In this scenario, the batch consists of 20 bad apples and 80 good apples. Since the selection is made with replacement, the total number of apples remains the same after each selection. Therefore, the probability of selecting a good apple on any given selection is simply the ratio of good apples to the total number of apples.
To start, we can calculate the probability of selecting a good apple on the first selection. Since there are 80 good apples and 100 apples in total, the probability is:
P(1st selection = good apple) = 80/100 = 4/5
Since the first apple is replaced before the second selection, the total number of apples remains the same for the second selection. Therefore, the probability of selecting a good apple on the second selection is also 4/5.
To calculate the probability of both events (selecting a good apple on the first selection and then on the second selection) happening together, we multiply the probabilities:
P(Select 2 good apples) = P(1st selection = good apple) * P(2nd selection = good apple)
= (4/5) * (4/5)
= 16/25
So, the probability of selecting 2 good apples when two are randomly selected with replacement is 16/25.