My Scando-Germanic friend, Odd Zahlen, often brings a die to class to answer multiple-choice final exam questions. Each multiple-choice question on this particular examination consists of three choices, and Odd decides to pick answer (a) if a 1 or 2 appears on a roll of the die, to pick (b) if a 3 or 4 appears on the die, or to pick (c) if a 5 or 6 appears. Assume that the correct answers are uniformly distributed among the choices (a), (b), and (c). What is the probability of obtaining exactly 5 correct answers on a ten question examination using this method?

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Respuesta :

ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2020-02-12T08:18:52+01:00

Answer:

[tex]P(A=5)= 0.1366[/tex]

Step-by-step explanation:

From each multiple-choice question, there consists three answers to each;

So the probability of picking, the correct answer as they are uniformly distributed among the choices (a), (b), and (c) will be;

P(correct answer) = [tex]\frac{1}{3}[/tex]

Now, to determine the probability of obtaining exactly 5 correct answers on a ten question examination using this method

Let use A as representative for the numbers of correct answers out of 10 questions that is being answered.

∴

[tex]P(A=5)= [\left \ {{10} \atop {5}} \right.][/tex] [tex](\frac{1}{3}) ^5[/tex] [tex](1-\frac{1}{3})^{10-5}[/tex]

[tex]P(A=5)= [\left \ {{10} \atop {5}} \right.](\frac{1}{3}) ^5 (\frac{2}{3}) ^5[/tex]

[tex]P(A=5)= 0.13657[/tex]

[tex]P(A=5)= 0.1366[/tex]