Can someone help me with this

In a multiple choice quiz there are 5 questions and 4 choices for each question (a, b, c, d). Robin has not studied for the quiz

Ahat [919]

Answer:

a) There is a 18.75% probability that the first question that she gets right is the second question.

b) There is a 65.92% probability that she gets exactly 1 or exactly 2 questions right.

c) There is a 10.35% probability that she gets the majority of the questions right.

Step-by-step explanation:

Each question can have two outcomes. Either it is right, or it is wrong. So, for b) and c), we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

In this problem we have that:

Each question has 4 choices. So for each question, Robin has a $\frac{1}{4} = 0.25$ probability of getting ir right. So $\pi = 0.25$ . There are five questions, so $n = 5$ .

(a) What is the probability that the first question she gets right is the second question?

There is a 75% probability of getting the first question wrong and there is a 25% probability of getting the second question right. These probabilities are independent.

So

$P = 0.75(0.25) = 0.1875$

There is a 18.75% probability that the first question that she gets right is the second question.

(b) What is the probability that she gets exactly 1 or exactly 2 questions right?

This is: $P = P(X = 1) + P(X = 2)$

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955$

$P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637$

$P = P(X = 1) + P(X = 2) = 0.3955 + 0.2637 = 0.6592$

There is a 65.92% probability that she gets exactly 1 or exactly 2 questions right.

(c) What is the probability that she gets the majority of the questions right?

That is the probability that she gets 3, 4 or 5 questions right.

$P = P(X = 3) + P(X = 4) + P(X = 5)$

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 3) = C_{5,3}.(0.25)^{3}.(0.75)^{2} = 0.0879$

$P(X = 4) = C_{5,4}.(0.25)^{4}.(0.75)^{1} = 0.0146$

$P(X = 5) = C_{5,5}.(0.25)^{5}.(0.75)^{0} = 0.001$

$P = P(X = 3) + P(X = 4) + P(X = 5) = 0.0879 + 0.0146 + 0.001 = 0.1035$

There is a 10.35% probability that she gets the majority of the questions right.

6 0

3 years ago

The sum of two numbers is 42. Their product is 360. What are the two numbers?

yKpoI14uk [10]

Those two numbers are 30 and 12.

30+12=42

and

30*12=360

:P

7 0

3 years ago

Read 2 more answers

On a farm in iowa lived grandpa bill in a big yellow house on the top of the hill. His 70th birthday was this very day. All of h

DENIUS [597]

Let g be the number of grandchildren, and d be the number of dogs. They both have only one head, so the number of heads is

$g+d=33$

Grandchildren have 2 legs, while dogs have 4. So, the total number of legs is

$2g+4d=84$

From the first equation (the one for the heads) we can derive

$g=33-d$

Substitute this into the second to get

$2g+4d=84 \implies 2(33-d)+4d=84 \iff 2d=18 \iff d=9$

So, there are 9 dogs and (from the first equation

$g=33-9=24$

8 0

3 years ago

What is the range of the given function?<br><br> {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}

Novay_Z [31]

Range is the set of possible output values of a function. In this case, it’s (-9, -3, 0, 5, 7).

8 0

3 years ago

Solve <img src="https://tex.z-dn.net/?f=%5Cfrac%7B2x-10%7D%7B4%7D" id="TexFormula1" title="\frac{2x-10}{4}" alt="\frac{2x-10}{4}

GREYUIT [131]

X = -1!
1. Factor out 2 from the expression : 2(x-5) / 4 = 3x
2. Reduce the fraction with 2 : x-5 / 2 = 3x
3. Multiply both sides of the equation by 2 : x-5=6x
4. Move the terms : x - 6x = 5
5. Collect like terms : -5x = 5
6. Divid both sides by -5
Hope this helps!

8 0

3 years ago