Probability Statistics

Question

Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manger assures you that 18 of the 44 boxes on the shelf have the secret decoder ring. The other 26 boxes on the shelf have a different gift inside.

if you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have a secret decoder ring? (Give answer as a decimal correct to four decimal

places.)

Answer 1

Hi Andrea,

So for this problem, it might help to think of the different cereals boxes as marbles in a bag. So imagine that you have 44 marbles in a bag, 18 of them are blue (the cereal boxes with the prize) and 26 are red.

Now we can gather that since we are taking cereal off of the shelf, no one is replacing the cereal we just took, meaning that each trial is dependant on the other and the first trial will change the probability of the second.

So if we have 44 marbles and 18 of them are blue, we have a probability of 18/44 of getting a blue marble on the first trial. Now the question is asking what the chances are of getting two in a row which means we are assuming that we got the blue marble the first trial.

If we took 1 blue marble from the bag in the first trial, that leaves us with 17 blue marble and a total of 43 marbles. Now when we go to take the second marble we will have a 17/43 chance of getting the blue marble.

So, the chance you have of getting both blue marbles (both cereal boxes with the prize), is 18/44 probability on the first trial, after which you have a 17/43 chance on the second trial. For both of these cases to happen in a row, you multiply the probabilities, so;

17/43 * 18/44

and you can evaluate that on a calculator to get the decimal.

I hope that helps!