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Sagot :
Let's begin by listing out the information given to us:
MARILYN (total, t) = 7 letters
At random implies every letter has an equal chance of being chosen
Number of trials (r) = 5 times
Number of "M" (n) = 1
Probability of choosing "M" once is given by:
[tex]P=\frac{n}{t}=\frac{1}{7}[/tex]what is the probability that the M is chosen exactly three times in five separate trials?
Of the 5 trials: 3 times "M" is picked, 2 times "other letters" are picked
[tex]\begin{gathered} P=(\frac{n}{t})^r\Rightarrow P=(\frac{1}{7})^3\cdot(\frac{6}{7})^2 \\ P=\frac{1}{343}\cdot\frac{36}{49}=\frac{36}{16807} \\ P=\frac{36}{16807}=0.002142\approx0.0021 \\ P=0.0021 \end{gathered}[/tex]
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