Question

there are seven nickels and six dimes in your pocket. you randomly pick a coin out of your pocket and then return it to your pocket. then you randomly pick another coin. find the probability that both coins are nickels.

Answer 1

Explanation:

a probability is airways the ratio

number of desired cases / number of totally possible cases

so, we have 7 nickels and 6 dimes. together that means we have 7+6 = 13 coins in total in the pocket.

since we return the coin from the first pull, we have the exact same probabilities for the second pull.

the 2 pulls are to be considered one combined event, so we need to combine the individual probabilities for the overall event probability.

the probabilty to pull a nickel in a pull is

7/13

7 desired possible outcomes over 13 total possible outcomes.

the combination of the probabilities of both pulls is simply their product.

so, the probability to pull 2 nickels is

7/13 × 7/13 = 49/169 = 0.289940828...