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kcla1996
 2 years ago
You have a 5question multiplechoice 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?
kcla1996
 2 years ago
You have a 5question multiplechoice 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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CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1To get the experimental probability, you have to run the experiment.

kcla1996
 2 years ago
Best ResponseYou've already chosen the best response.0can i just do it by writing a binomial

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Yes, this is a binomial situation.

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Consider 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.

kcla1996
 2 years ago
Best ResponseYou've already chosen the best response.010*9/4^3 this is what i got.....

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Mmm, some of those numbers are right, but aren't in the right places...

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0exactly 3 right out of 5 means 3 right, 2 wrong and \(\dbinom{5}{2}\) ways to do it

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Number of ways to get 3 out of 5 = 5C3 = 5C2 = 10, so the 10 in right.

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1... *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.

kcla1996
 2 years ago
Best ResponseYou've already chosen the best response.0so can you help me write the answer?

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1See http://stattrek.com/probabilitydistributions/binomial.aspx?Tutorial=Stat for derivation of the binomial formula.

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1I think you have everything you need; just multiply it all together.

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1There 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.

kcla1996
 2 years ago
Best ResponseYou've already chosen the best response.0is 10 x (.25)^3 x(0.75)^2 the answer

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Makes 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/probabilityrules.aspx?Tutorial=Stat

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Does 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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