The chances that a student will get 7 marks out of 10 in first attempt of a certain Quiz while attempting Quiz on BlackBoard LMS is 40%. Suppose that 20 students are selected at random then find a probability that i)Exactly 12 students will get 7 marks out 10 in the Quiz. ii)Fewer than 10 students will get 7 marks out 10 in the Quiz. iii)At least 5 students will get 7 marks out 10 in the Quiz.

i)

ii)

iii)

Step-by-step explanation:

Let's start by defining the random variable ⇒

'' Number of students that will get 7 marks out of 10 in first attempt of a certain Quiz while attempting Quiz on BlackBoard LMS ''

is a discrete random variable.

The probability of a randomly selected student getting 7 marks out of 10 is 0.4

(This is a data from the question).

Now, if we assume independence between the students while they are doing the Quiz and also we assume that this probability remains constant , we can modelate as a binomial random variable ⇒

~ Bi (n,p)

Where ''n'' and ''p'' are the parameters of the variable.

''n'' is the number of students attempting the Quiz and ''p'' is the probability that a student will get 7 marks out of 10 which is 0.4 ⇒

~ Bi (20, 0.4)  in the question.

The probability function for is

   (I)

Where is the combinatorial number define as

Replacing the parameters in the equation (I) ⇒

   (II)

For i) we need to find

Then, we only need to replace by in equation (II) ⇒

For ii) we need to calculate

This probability is equal to ⇒ and to calculate it we need to sum

We can do it summing each term or either using any program.

The result is

Finally for iii) we need to find  ⇒

This probability is equal to ⇒ ⇒

Again we can find each term by using the equation (II) or either using a program. The result is

expression #3 is not equivalent. the others are.

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: