Coin word equation

Question

Michelle has a purse that contains 7 silver coins and 5 gold coins. She draws one coin at random and then draws a second coin. What is the probability that the first coin is gold and the second coin is silver if the coins are drawn with replacement and without replacement?

Answer 1

With replacement

(7/12)(5/12) = ?

Without preplacement

(7/12)(5/11) = ?

Answer 2

Hi Hanna.

If the coins are drawn WITHOUT replacement:

The probability of the first coin drawn being gold is 5/12 and the probability that the 2nd coin drawn being silver is 7/11. Therefore the probability of both together is 5/12 * 7/11 or 35/132

If the coins are drawn WITH replacement:

The probability of the first coin drawn being gold is 5/12 and the probability that the 2nd coin drawn being silver is 7/12. Therefore the probability of both together is 5/12 * 7/12 or 35/144

Hope this helps!