How to Find the Probability of Two Events Occuring Together

Probability 5 Comments

Sample problem: “85% of employees have health insurance; out of those 85%, 45% had deductibles higher than $1,000. What percentage of people had deductibles higher than $1,000?”

The key to these problems is the phrase “Out of this group” or “Of this group…” which tells you the events are dependent. You can solve these probability questions in only two steps.

Step 1: Convert your percentages of the two events to decimals. In the above example:

85% = .85
45% = .45

Step 2: Multiply the decimals from step 1 together:

.85 x .45 = .3825 or 38.35 percent.

That’s it!

Related posts:

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  3. How to Use a Probability Tree for Probability Questions
  4. How to Find the Probability of Group Members Choosing the Same Thing
  5. How to find the Probability of an Event, Given Another Event
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5 Responses to “How to Find the Probability of Two Events Occuring Together”

  1. Angie Widdows said:

    Sep 17, 09 at 6:26 pm

    this explanation was helpful, although I think that it could go into a bit more depth. It does not explain where, if at all, the $1000 fits into place. Why have it in the question if it does not pertain to the answer.

  2. Stephanie said:

    Sep 18, 09 at 6:50 am

    Angie,

    I agree. I added a little more info–hopefully that helps to clarify,

    Stephanie

  3. Lisa Barcomb said:

    Oct 25, 09 at 6:21 pm

    Yeah you are right it could have given more information regarding the problems bur I guess if you know the difference between dependent and independent you should not have a problem.

  4. Grant said:

    Oct 31, 11 at 2:31 pm

    Also, in the problem you ask “how many people had deductibles higher than $1000,” not “what percentage of people” or “what’s the probability that…”

    We can’t answer your questions without knowing how many employees are at the company.

  5. Stephanie said:

    Oct 31, 11 at 3:17 pm

    You are correct! Thank you for the correction.

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