Counting and Probability: Word Problems

Probability: Word Problems

As with other types of word problems, the best approach to navigating and solving probability word problems is to translate them from words to math.

The first thing to do, though, is to figure out what the problem is asking you to do. That sounds simple, but so many of us forget to do it, making our math lives harder in the end. Are you being asked to find probability? Odds in favor? Odds against?

Something else that you might find helpful in some cases is to draw yourself a picture. Statisticians and math teachers LOVE the classic "we have a bag of marbles" problems. If it helps, draw the bag of marbles so you can see what you're working with.

Let's look at a few examples.

Rewriting as a ratio yields $\boxed{23:41}$.

Rewrite as a ratio and simplify: $$44:20 = \boxed{11:5}.$$

$$\begin{align}P(\text{coconut and then chocolate}) &= \frac{7}{64}\cdot\frac{23}{63} \\ &= \boxed{\frac{161}{4032}}\end{align}$$

(Video) Probability Word Problem

by Mega Mind Academy

Mega Mind Academy has an excellent video explaining how to approach probability word problems.

(Video) Probability Word Problems (Simplifying Math)

by Eric Buffington

This is a great video that gives you a refresher in probability as a whole. He includes a quick recap on probability, defining it as $\frac{\text{Favorable Outcome}}{\text{All Possible Outcomes}}$.

$\large{\text{Summary}}$

This is about as basic as probability gets, which is great. He gives an example of finding the probability of rolling a $3$ on a $6$ sided die. With these two factors, he reminds the watcher that the favorable outcome does not need to appear in the outcome.

Then, he goes into calculating probability, and does a regular example to transition into word problems. When he starts the word problems, he goes into them full force. He does several examples, including a "tricky" question at the end. Watch for yourself! I highly suggest watching this to get a better grasp on word problems.