Binomial probability states that the probability of x successes on n repeated trials in an experiment which has two possible outcomes can be obtained by
(nCx).(p^x)⋅((1−p)^(n−x))
Where success on an individual trial is represented by p.
In the given question, obtaining heads in a trial is the success whose probability is 1/2.
Probability of 6 heads with 6 trials = (6C6).((1/2)^6).((1/2)^(6–6))
= 1/(2^6)
= 1/64
To the nearest thousand is 23,000 and the nearest ten thousand is 20,000
Answer:
a) p=0.2
b) probability of passing is 0.01696
.
c) The expected value of correct questions is 1.2
Step-by-step explanation:
a) Since each question has 5 options, all of them equally likely, and only one correct answer, then the probability of having a correct answer is 1/5 = 0.2.
b) Let X be the number of correct answers. We will model this situation by considering X as a binomial random variable with a success probability of p=0.2 and having n=6 samples. We have the following for k=0,1,2,3,4,5,6
.
Recall that
In this case, the student passes if X is at least four correct questions, then

c)The expected value of a binomial random variable with parameters n and p is
. IN our case, n=6 and p =0.2. Then the expected value of correct answers is 
1. -3x and -6x
2. 21 and -13
3. 21 and -13
4. -10b and 6b, 15 and -5
5. -20 and 30, 4c and -2c