Probability problem

Hey im having some problems with probability and here are the two homework questions.

1)What is the probability that you will pass a test and get at least 4 questions correct by randomly guessing on each question of a 6 question quiz multiple choice quiz with 5 choices for each question.

2) Every year at least 5 million people die of tobacco related causes, assume that the distribution is normal with a population mean of 5 million and a standard deviation of 2 million...find the probability that more than 4 million people will die of tobacco related causes and find the 75th percentile of the distribution of tobacco related deaths.

any help is appreciated!

1)What is the probability that you will pass a test and get at least 4 questions correct by randomly guessing on each question of a 6 question quiz multiple choice quiz with 5 choices for each question.

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Use the binomial probability. \(\displaystyle \sum_{k=4}^{6}\binom{6}{k}\left(\frac{1}{5}\right)^{k}\left(\frac{4}{5}\right)^{6-k}\)

2) Every year at least 5 million people die of tobacco related causes, assume that the distribution is normal with a population mean of 5 million and a standard deviation of 2 million...find the probability that more than 4 million people will die of tobacco related causes and find the 75th percentile of the distribution of tobacco related deaths.

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Use \(\displaystyle z=\frac{x-{\mu}}{\sigma}\) and look up the probability in a z table.

Hello, coheedfan1990!

I'll go through #1 and explain galactus' answer in baby steps . . .

1)What is the probability that you will pass a test and get at least 4 questions correct
by randomly guessing on each question of a 6-question multiple-choice quiz with 5 choices for each question?

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\(\displaystyle \text{On any question: }\;\begin{Bmatrix}P(\text{right}) &=& \frac{1}{5} \\ \\[-3mm] P(\text{wrong}) &=& \frac{4}{5}\end{Bmatrix}\)


"Pass the test" means: "at least 4 right".
"At least 4 right" means: "4 right or 5 right or 6 right".


So we must consider the three cases.

[1] 4 right (and 2 wrong)
. . \(\displaystyle P(\text{4 right}) \:=\:{6\choose4}\left(\frac{1}{5}\right)^4\left(\frac{4}{5}\right)^2 \:=\:\frac{240}{15,\!625}\)

[2] 5 right (and 1 wrong)
. . \(\displaystyle P(\text{5 right}) \:=\:{6\choose5}\left(\frac{1}{5}\right)^5\left(\frac{4}{5}\right)^1 \:=\:\frac{24}{15,\!625}\)

[3] 6 right (and 0 wrong)
. . \(\displaystyle P(\text{6 right}) \;=\;{6\choose6}\left(\frac{1}{5}\right)^6\left(\frac{4}{5}\right)^0 \:=\:\frac{1}{15,\1625}\)


\(\displaystyle \text{Therefore: }\;P(\text{pass}) \;=\;\frac{240}{15,\!625} + \frac{24}{15,\1625} + \frac{1}{15,\!625} \;=\;\frac{265}{15,\!625} \;=\;\frac{53}{3125} \;\approx\;1.7\%\)

coheedfan1990 said:

2) Every year at least 5 million people die of tobacco related causes, .....

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Well, one of these years it'll be 5,000,001 ... cause I can't quit :roll: