(a) If you spent 10 minutes repeatedly shaking and throwing down a pair of coins, would you expect to see two heads come up at least once? (b) If you spent an hour shaking a handful of 10 coins and throwing them down, would you expect to see all 10 come up heads at least once? (c) If you stirred a box of 10,000 coins and tossed them repeatedly on the floor all day long, would you expect to see all 10,000 appear as heads at least once?
Solution 48E Step 1: a) The combinations which we will get while tossing two coins will be HH,HT,TH and TT Where T stands for tail and H stands for the head. So, total 4 combinations we will get and the probability of getting two head combination is, P = ¼. If we spent 10 minutes for tossing two coins repeatedly, there is a possibility of getting this two head combination at least once. Step 2: 10 b) In the case of 10 coins, the total number of combinations possible will be 2 . We will get all heads combinations only once in this 2 combination. The probability of getting all heads, P = 1/ 2 10 Within the one hour time, we should look for maximum number of experiments in order to get all possible combinations. If we do maximum tries, then there is a possibility of getting all head combination. The probability of getting all head combinations for 10 coins will be less than that of the probability of getting all head combinations for 2 coins.