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morpeh [17]
3 years ago
14

A student takes a true-false test that has 10 questions and guesses randomly at each answer. Let X be the number of questions an

swered correctly. Find P(Fewer than 3). Round your answer to 2 decimal places.
Mathematics
1 answer:
Dvinal [7]3 years ago
4 0

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;

P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....

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)

=  \binom{10}{0}\times 0.50^{0} \times (1-0.50)^{10-0}+ \binom{10}{1}\times 0.50^{1} \times (1-0.50)^{10-1}+ \binom{10}{2}\times 0.50^{2} \times (1-0.50)^{10-2}

=  1 \times 0.50^{10} + 10 \times 0.50^{10} +45 \times 0.50^{10}

=  0.05

Hence, the P(Fewer than 3) is 0.05.

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Step-by-step explanation:

Cost of one child ticket = $1.75

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Total receipts worth = $1184.75

Let,

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Multiplying Eqn 1 by 1.75

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Putting y=224 in Eqn 1

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Keywords: linear equation, subtraction

Learn more about linear equations at:

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