Multiply this expression :: -2/7 • (-3 5/8)

1. A student is taking a multiple-choice exam in which each question has four choices. Assume that the student has no knowledge

LenKa [72]

Answer:

a) 0.001 = 0.1% probability that she will get five questions correct.

b) 0.0156 = 1.56% probability that she will get at least four questions correct.

c) 0.2373 = 23.73% probability that she will get no questions correct.

d) 0.8965 = 89.65% probability that she will get no more than two questions correct.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either she gets it correct, or she does not. The probability of getting a question correct is independent of any other question, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

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

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

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

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

And p is the probability of X happening.

There are five multiple choice questions on the exam.

This means that $n = 5$

She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box.

This means that $p = \frac{1}{4} = 0.25$

a. Five questions correct?

This is $P(X = 5)$ . So

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

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

0.001 = 0.1% probability that she will get five questions correct.

b. At least four questions correct?

This is:

$P(X \geq 4) = P(X = 4) + P(X = 5)$

So

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

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

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

$P(X \geq 4) = P(X = 4) + P(X = 5) = 0.0146 + 0.001 = 0.0156$

0.0156 = 1.56% probability that she will get at least four questions correct.

c. No questions correct?

This is P(X = 0). So

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

$P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373$

0.2373 = 23.73% probability that she will get no questions correct.

d. No more than two questions correct?

This is:

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$ . So

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

$P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373$

$P(X = 1) = C_{5,0}.(0.25)^{1}.(0.75)^{4} = 0.3955$

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

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2373 + 0.3955 + 0.2637 = 0.8965$

0.8965 = 89.65% probability that she will get no more than two questions correct.

3 0

3 years ago

Please help show my work

lara [203]

Answer:

i cant really see what it says

Step-by-step explanation:

8 0

2 years ago

A locker combination has three nonzero digits, and digits cannot be repeated. The first two digits are 1 and 2. What is the prob

lions [1.4K]

The probability of the last digit is 3 is1/7

5 0

2 years ago

On the surface of the moon, the value of g is 1.67 m/s2. What is the horizontal distance traveled during a 2.00-meter high jump

rodikova [14]

To solve this question, you need to find how long jump is. For 2m high with 1.67 m/s2 it would be:

h= 1/2 gt^2
2= 1/2 * (1.67) t^2
t^2= 1.67
t= 1.29

If the speed is 20 mph and the jump is 2 second, the distance traveled would be:
20 miles/ hour * 1.29 second * (1 hour/3600second)= 0.007179 miles

If you need to convert it to meter then: 0.007179 mile * 1609.34meter/ mile= 11.55 meter

8 0

2 years ago

Complete the sequence: 1, 1, 2, 3, 5, ____, ____, ____.

Elza [17]

Answer:

8, 13, 21

Step-by-step explanation:

This is a part of the Fibonacci sequence. it is where you add the two previous numbers together to get the third.

Ex.

1+1 = 2

1+2 = 3

7 0

3 years ago

Multiply this expression :: -2/7 • (-3 5/8)​

Multiply this expression :: -2/7 • (-3 5/8)