Question

A walet containts 3 quarters and 2 dimes, Clara selects one coin from the watlet, replaces e, and then selects a second coin. Let A = pthe first coin selected is a dime?. and Let B = fthe second coin selected is a dime] Which of the following statements is true? A and B are independent events, as P(B∣A)=P(B). A and B are independent events, as P(B)A)=P(B) A and B are dependent events, as P(B/A)=P(B) A and B are dependent events, as P(B,A)=P(B)

Answer 1

A and B are dependent events, as the conditional probability of B given A is not equal to the probability of B.

Step-by-step explanation:

A and B are dependent events, as P(B|A) is not equal to P(B).

To determine whether events A and B are independent or dependent, we need to compare the conditional probability of B given A (P(B|A)) to the probability of B (P(B)). If P(B|A) = P(B), then the events are independent. However, if P(B|A) != P(B), then the events are dependent.

In this case, let's calculate the probabilities:

P(A) = Number of ways to select a dime / Total number of coins = 2 / 5 = 0.4

P(B|A) = Number of ways to select a dime as the second coin given that the first coin was a dime / Total number of coins remaining after selecting a dime in the first draw = 1 / 4 = 0.25

P(B) = Number of ways to select a dime / Total number of coins = 2 / 5 = 0.4

Since P(B|A) != P(B) (0.25 != 0.4), we can conclude that events A and B are dependent.