Andrew has 7 20c coins and 5 50c coins in his piggy bank. What is the smallest number of coins he might have to shake out to be certain of having 2 50c coins?

I don't know what country you are in, but I am not aware of "20c coins."

To be4 absolutely certain of getting 2 50c coins, you would have to shake out 9 coins. This is assuming the worst scenario that all the 20c coins come out first.

To find the smallest number of coins Andrew might have to shake out to be certain of having 2 50c coins, we need to consider the worst-case scenario.

First, let's count the number of 50c coins Andrew currently has, which is 5.

Now, we need to determine the minimum number of coins he needs to shake out, assuming he shakes out all the 20c coins first. This will ensure that he maximizes the number of 50c coins that he still has in the piggy bank.

Since each shake will give us one 50c coin, we need to shake out at least 2 coins to guarantee having 2 50c coins.

Additionally, for each 20c coin we shake out before finding the 2nd 50c coin, we reduce the chance of finding a 50c coin, since they are being replaced with 20c coins.

Therefore, the smallest number of coins Andrew might have to shake out to be certain of having 2 50c coins is 2.

To find the smallest number of coins Andrew might have to shake out to be certain of having 2 50c coins, we need to consider the worst-case scenario.

Let's analyze the coins Andrew currently has:
- He has 7 20c coins and 5 50c coins.

We want to make sure Andrew shakes out the fewest number of coins to get 2 50c coins. So, Andrew will shake out all the 20c coins first, and then shake out enough coins to ensure that at least 2 of the remaining coins are 50c coins.

To be certain of having 2 50c coins, we need to assume that Andrew shakes out all of his 20c coins, leaving us only with the 50c coins to consider.

Andrew currently has 5 50c coins, so at most, he would need to shake out 3 more coins to guarantee having 2 50c coins. The worst-case scenario is that he shakes out all 3 additional coins and none of them are 50c coins.

Therefore, the smallest number of coins Andrew might have to shake out is 3.

Note: This approach assumes that there are only 20c and 50c coins in Andrew's piggy bank and that we are considering all possible outcomes.