Answer :
a) The probability that a student does more than 8 mistakes is 0.36.
b) The probability that a student makes 5 or more mistakes is 0.73.
c) A student makes at most 8 mistakes is 0.64.
d) Options a and Options c are complimentary occurrences by definition.
There are 16 multiple-choice questions in a driving test. Each of the 16 responses is either correct or incorrect. Assume that the likelihood that a student will make less than five mistakes on the test is 0.37 so the likelihood that they will make between five and eight mistakes (inclusive) is 0.27.
Let X be the number of mistakes,
P(X < 5) = P(X ≤ 4) = 0.27
P(5 ≤ X ≤ 8) = 0.37
The probability of each of the following outcomes.
a) A student does more than 8 mistakes,
P(X > 8)
P(X > 8) = 1 - P(X ≤ 4)
P(X > 8) = 1 - (P(X ≤ 4) + P(5 ≤ X ≤ 8))
P(X > 8) = 1 - (0.27 + 0.37))
P(X > 8) = 1 - 0.64
P(X > 8) = 1 - 0.64
P(X > 8) = 0.36
b) The probability that a student makes 5 or more mistakes is,
P(X ≥ 5) = 1 - P(X < 5)
P(X ≥ 5) = 1 - 0.27
P(X ≥ 5) = 0.73
c) A student makes at most 8 mistakes,
P(X ≤ 8) = 1 - P(X > 8)
P(X > 8) = 0.36
P(X ≤ 8) = 1 - 0.36
P(X ≤ 8) = 0.64
d) The probability that an event won't happen is the exact opposite of the complement of it happening.
Options a and Options c are complimentary occurrences by definition.
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