Probability

Question

A box contains 4 plain pencils and 4 pens. A second box contains 7 color pencils and 3 crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon from the second box are selected?

Answer 1

Hi Ashley! Let's break this down.

 

So, the first thing we need to recognize is that we have two separate boxes. So what we choose from the first box has no impact on what we choose from the second box. So our two choices from the two boxes are what we would call independent events.

 

Now, what is the probability of getting a pen from the first box? Well, it's 4 pens divided by the total number of items in the box, or 4/4+4 = 4/8 = 1/2 = 0.5 or 50%.

 

What is the probability of getting a crayon from the second box? Similarly, it's 3/3+7 = 3/10 = 0.3 or 30%.

 

Now what about the probability of both of these happening, one after the other? Because the events are independent we can just multiply the probabilities together. There was a 50% chance we got a pen from the first box and then a 30% chance we got a crayon from the second box. So there was a 50% * 30% = 0.5 * 0.3 = 0.15 or 15% chance that we had both happen.

 

Also note that whether we choose an item from the first or second box first does not impact our answer (that is, the order of our choices doesn't matter).

 

Hope this helps!