One day your teacher surprised you with a 22-question multiple-choice quiz. Each question has 4 possible answers, only one of which is correct. What is the probability that you will guess at least 1 correctly?

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Answer 1 · 2018-03-13T18:01:22

#P("at least "1 " correct") = 1-P("all wrong")#

#=1-(3/4)^22#

#=0.998#

#=99.8%#

The probability of "at least 1 correctly" means:

#1," "or 2," "or 3 ," " 4," "......or 22 # correct.
This would be very tedious to work out.

However, the only outcome not included is the probability of none correct.

#P("none correct") = P("all wrong")#

#= P (WxxWxxWxxWxxW ....... xxW# for #22# questions

For each question,:

#P("correct") = 1/4# and #P("wrong") = 3/4#

#P("all wrong") = 3/4xx3/4xx3/4 ,..... xx3/4# for #22# questions

#P("all wrong")= (3/4)^22#

The sum of all the probabilities is always #1#.

#P("at least "1 " correct") = 1-P("all wrong")#

#=1-(3/4)^22#

#=0.998#

This means a #99.8%# chance of at least one question being correct,