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)

Question

Responses

727
Start Fraction 7 over 27 End Fraction

23
Start Fraction 2 over 3 End Fraction

29
Start Fraction 2 over 9 End Fraction

19
Start Fraction 1 over 9 End Fraction

Answer 1

The probability of picking a dime on any one draw is 1/3, since there is only one dime out of the three coins.

The probability of picking a dime exactly twice in three draws can be calculated as follows:
Probability of picking a dime on the first draw and another dime on the second draw, and then any coin on the third draw:
(1/3) * (1/3) * (2/3) = (2/27)

Since there are three possible scenarios for picking a dime exactly twice (dime-dime-anything, dime-anything-dime, anything-dime-dime), we multiply the result by 3:
(2/27) * 3 = 6/27 = 2/9

Therefore, the probability that a dime is picked exactly twice is 2/9.

So the correct response is:
29
Start Fraction 2 over 9 End Fraction