A nickel, a penny, and a dime are placed inside a bag. One coin is randomly picked three times. If the coin is replaced after each draw, what is the probability that a dime is picked exactly twice?(1 point)
Responses
727
Start Fraction 7 over 27 End Fraction
19
Start Fraction 1 over 9 End Fraction
29
Start Fraction 2 over 9 End Fraction
23
Start Fraction 2 over 3 End Fraction
The probability of picking a dime on any given draw is 1/3, since there are three coins and only one is a dime.
Therefore, the probability of picking a dime exactly twice in three draws is:
(1/3) * (1/3) * (2/3) = 2/27
So, the correct answer is:
21
Start Fraction 2 over 27 End Fraction
this is not one of the answers
Apologies for the error in calculation. Let's try again:
The probability of picking a dime on any given draw is 1/3, since there are three coins and only one is a dime.
To pick a dime exactly twice in three draws, we can consider the following scenarios:
1. Dime is picked on the first and second draw, and not picked on the third draw.
2. Dime is picked on the first and third draw, and not picked on the second draw.
3. Dime is picked on the second and third draw, and not picked on the first draw.
The probability for each scenario is: (1/3) * (1/3) * (2/3) = 2/27
Since there are three possible scenarios, we add the probabilities: 2/27 + 2/27 + 2/27 = 6/27 = 2/9
Therefore, the correct answer is:
29
Start Fraction 2 over 9 End Fraction