For each question, there are only two possible outcomes. Either she guesses the correct answer, or she does not. The probability of guessing the correct answer for a question is independent of other questions. So we use the binomial probability distribution 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.

Seven questions:

This means that $n = 7$

Each question has four choices.

Abby guesses, which means that $p = \frac{1}[4} = 0.25$

Find the probability to the nearest thousandth, that Abby gets exactly three questions correct.

This is P(X = 3).

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

$P(X = 3) = C_{7,3}.(0.25)^{3}.(0.75)^{4} = 0.173$

8 0

3 years ago

A pentomino is made up of five squares where two squares are joined along an entire side. Two pen- tominos are the same if they

Studentka2010 [4]

There are 12 such shapes. One can start with two squares, adding squares around the edge and rejecting shapes that have been previously seen. Repeating until you have 5 squares results in 12 distinct shapes.

_____

2 shapes are possible with 3 squares: L, I

5 shapes are possible with 4 squares: L, I, N, T, O

5 0

3 years ago

There are 24 girls in a class. The ratio of girls to boys is 3:8.

dangina [55]

Answer:

64 boys.

Step-by-step explanation:

There are 3 girls for every 8 boys.

24/3 = 8

8 * 8 = 64

7 0

3 years ago

A line passes trough the point { 0, -3/2} and has a slope of 1/2. what is the equation of the line?

Luden [163]

Solutions: x=1.

Hope this helps!

6 0

3 years ago