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Answer:
P(Fewer than 3) = 0.05.
Step-by-step explanation:
We are given that a student takes a true-false test that has 10 questions and guesses randomly at each answer.
The above situation can be represented through Binomial distribution;
where, n = number of trials (samples) taken = 10 questions
r = number of success = fewer than 3
p = probability of success which in our question is probability
that question is answered correctly, i.e; 50%
<u>LET X = Number of questions answered correctly</u>
So, it means X ~ Binom(n = 10, p = 0.50)
Now, Probability that Fewer than 3 questions are answered correctly is given by = P(X < 3)
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
=
=
= 0.05
Hence, the P(Fewer than 3) is 0.05.