A multiple-choice test has 10 questions. Each question has 5 choices and only one of which is correct. If a student guesses the answer for each question find the probability that the students gets exactly 8 questions correct.
+421 The favorable possibilities will be 1 choice out of 5, a 1/5 probability of getting a question right, 4/5 for getting a question wrong. Thus by the binomial probability distribution,
P(8 correct; 2 wrong)
$(1/5)^8 \cdot (4/5)^2 \cdot {10 \choose 8}$
Make sure you see why this works! This is an AND (U) Probability! What is the formula and be sure to include the unfavorable attempts too!!
This gives you a result of $\frac{144}{1953125}$, or $0.000073728,$ or in standard form, $7.3728 \times 10^{-5}$, or $0.0073728$%
