n 4) There are eight nickels and eight dimes in your pocket. You randomly pick a coin out of your pocket and then return it to your pocket. Both times the coin is a nickel.

Answer 1

The probability of picking a nickel from a pocket containing eight nickels and eight dimes is:

P(nickel) = 8 / (8 + 8) = 1/2

Since the coin is returned to the pocket after each pick, the probability of picking another nickel on the second pick is also 1/2.

Therefore, the probability of picking two nickels in a row is:

P(nickel, then nickel) = P(nickel) * P(nickel|nickel)

where P(nickel|nickel) is the conditional probability of picking a nickel given that a nickel was already picked on the first pick.

Since the coin is returned to the pocket after each pick, the probability of picking a nickel on the second pick is the same as the probability of picking a nickel on the first pick, which is 1/2. Therefore:

P(nickel, then nickel) = (1/2) * (1/2) = 1/4

Therefore, the probability of randomly picking a coin from the pocket twice and getting two nickels in a row is 1/4 or 0.25.