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## kcla1996 3 years ago You have a 5-question multiple-choice test. Each question has four choices. You don’t know any of the answers. What is the experimental probability that you will guess exactly three out of five questions correctly?

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1. CliffSedge

To get the experimental probability, you have to run the experiment.

2. kcla1996

can i just do it by writing a binomial

3. CliffSedge

Yes, this is a binomial situation.

4. CliffSedge

Consider the probability of success for each trial, the number of trials, the number of successes sought, and the number of combinations of getting that many successes.

5. kcla1996

10*9/4^3 this is what i got.....

6. CliffSedge

Mmm, some of those numbers are right, but aren't in the right places...

7. satellite73

exactly 3 right out of 5 means 3 right, 2 wrong and \(\dbinom{5}{2}\) ways to do it

8. CliffSedge

Number of ways to get 3 out of 5 = 5C3 = 5C2 = 10, so the 10 in right.

9. CliffSedge

... *is right. 3 successes = (.25)^3 with a 25% chance of getting any question correct at random. 2 failures = (.75)^2 for similar reasons as above.

10. kcla1996

so can you help me write the answer?

11. CliffSedge

See http://stattrek.com/probability-distributions/binomial.aspx?Tutorial=Stat for derivation of the binomial formula.

12. CliffSedge

I think you have everything you need; just multiply it all together.

13. kcla1996

i really not get it.

14. CliffSedge

There are ten ways to get 3 out of 5. (use combinations formula 5choose3) To get 3 successes with a 25% chance each, that's 0.25 × 0.25 × 0.25 = (0.25)^3 To also get the 2 failures with a 75% chance: 0.75 × 0.75 = (0.75)^2 Altogether, the probability is 10 × (0.25)^3 ×(0.75)^2.

15. kcla1996

is 10 x (.25)^3 x(0.75)^2 the answer

16. CliffSedge

Makes sense to me. 10 ways to have 3 successes and 2 failures multiplied by the probability of having 3 successes multiplied by the probability of having 2 failures. See also http://stattrek.com/probability/probability-rules.aspx?Tutorial=Stat

17. kcla1996

but is it the answer

18. CliffSedge

Does it make sense to you? Why do you still have doubts? Follow those links to that website I posted and study until you understand why the probability is computed that way.

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