Finding a Probability

Question

You decide to start taking coins out of your piggy bank. Currently, your piggy bank has 46 coins, of which 11 are toonies and 7 are loonies. Suppose that when you take a coin out, you do not put it back in the piggy bank; you are picking coins without replacement. (Round your answers to 4 decimal places, if needed.)

(a) What is the probability that the third coin you pick is the first toonie you find?

(b) What is the probability that at least one of the first two coins you pick is a toonie?

(c) What is the probability that the first three coins you pick are all either loonies or toonies?

Answer 1

Since you are replacing the coin each time, the probability for each "draw" of a particular coin remains the same for every drawl you make. The next thing you need to do is calculate the probabilities of 2 thing:1) p(drawing a Toonie, or T going forward), and the p(drawing a Loonie, or L going forward). Now notice that the (number of T's) + (the number of L's) is < the total number of coins, so calculate the probability that you don't draw either a T or an L. To do that you just need to find how many coins are neither a T or a L.

To solve any of the three problems use the three probabilities you just calculated in addition to any 'special situations you may need. For example (a) What is the probability that the third coin you pick is the first T you find?

a) If the 3rd draw is the first T, that means draws 1 & 2 are not T's: Since there are 11 T's, there must be 46-11=35 coins that are not T's, what's the probability of choosing 1 of those 35 coins? Now you just multiply the probabilities of each draw: P(not T)*P(not T)* P(T). Parts b) and c) use similar logic.

Try writing the problem in terms of probabilities, like I did for the first one.

HINT for part b) Since your asked to find the prob of "at least 1 of first 2 is a T", remember what that means (i.e. you can either get 1 T or 2 T's in your first two draws).