Question

I have a hat that contains six nickels and five pennies. I draw coins from the hat at random, without replacement. Find the probability that after drawing four coins, I have removed at most two pennies from the hat.

Answer 1

Answer:

53/66

Explanation:

We can use complementary counting to find the probability of picking the outcomes we don't want, and then subtracting that from the whole. The outcomes we don't want are PPPP and PPPN.

Probability of picking PPPP: 5/11 * 4/10 * 3/9 * 2/8 = 120/7920 = 1/66

Probability of picking PPPN: 5/11 * 4/10 * 3/9 * 6/8 = 360/7290 = 3/66

We can arrange PPPN in four different ways (PPPN, PPNP, PNPP, NPPP) so we need to multiply by 4, giving 12/66.

The total of these two probabilities is 13/66. Subtracting from 66/66, the answer is 53/66.