A sample of three coins is selected without replacement from a handful of eight coins that consists of four 10ccoins and four 20c coins. What is the probability that the sample contains at least two 10c coins?

To solve this problem, we need to calculate the probability of getting at least two 10c coins when drawing three coins from a pool of eight (four 10c coins and four 20c coins). This means we need to calculate the probability of getting exactly two 10c coins and the probability of getting exactly three 10c coins, and then add these two probabilities together.

1. Calculate the probability of getting exactly two 10c coins:

   This can happen in 3 ways: TT2, T2T, 2TT (where T represents a 10c coin and 2 represents a 20c coin). The probability of each of these events is (4/8) * (3/7) * (4/6) = 1/7. Since there are 3 such events, the total probability of getting exactly two 10c coins is 3 * 1/7 = 3/7.

2. Calculate the probability of getting exactly three 10c coins:

   This can only happen in one way: TTT. The probability of this event is (4/8) * (3/7) * (2/6) = 1/14.

3. Add the probabilities from steps 1 and 2 to get the total probability of getting at least two 10c coins:

   3/7 + 1/14 = 7/14 = 0.5.

So, the probability that the sample contains at least two 10c coins is 0.5 or 50%.