Question

Michael has 3 quarters, 2 dimes, and 3 nickels in his pocket. He randomly draws two coins from his pocket, one at a time, and they are both dimes. He says the probability of that occurring is 1 4 because 2 of the 8 coins are dimes. Is he correct? Explain.

Answer 1

I know someone already put in a correct answer but here’s the one I wrote,

He is incorrect because the probability of pulling a dime out of his pocket is 2/8 but if he wishes to pull a dime again his probability would be 1/7. To find the total probability you would need to times the numbers which then gives you 2/56 but if you simplify you get 1/28 meaning you have a 1 in 28 chance of pulling two dimes in a row.

Answer 2

Answer: No. Choosing two dimes are dependent events. The probability of choosing the first dime is 1/4 and the probability of choosing the second dime is 1/7. The probability that both coins are dimes is (1/4)(1/7) = 1/28.