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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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2 years ago
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elixir [45]
<span>Answer: 100,000,000 + 3,000,000 + 700,000 + 20,0000 + 7,0000 + 400 + 90 + 5 = 103,727,495
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<span>Explanation:
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<span>1) The expanded form of a number is the split of the number using every digit muliplied by its place value.
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<span>2) The first (left most) digit of the given number is 1. It is in the hundred millions place. So, it represents 100,000,000 which is the first number in the expanded form.
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<span>3) The second digit (from lef to right) is 0, so its value is 0, and you do not include it in the expanded form.
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<span>4) The third digit (from the left to the right) is 3. It is in the place of the millions, so its value is 3,000,000.
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<span>5) Next number from the left is 7 and it is in the hundred thousands place, so its value is 700,000.
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<span>6) Next is 2, in the ten thounsands place => 20,000
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<span>7) Next is 7 in the thousands => 7,000
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</span><span>10) Finally 5 in the ones => 5.</span>
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</span><span>Then number the number is: 100,000,000 + 3,000,000 + 700,000 + 20,000 + 7,000 + 400 + 90 + 5</span>

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