Question

x is a binomial random variable. (Give your answers correct to three decimal places.)
(a) Calculate the probability of x for: n = 1, x = 0, p = 0.15
P(x) = Changed: Your submitted answer was incorrect. 0.15 x 0 = 0 .

(b) Calculate the probability of x for: n = 3, x = 3, p = 0.15
P(x) = Incorrect: Your answer is incorrect. . 0.15 x 3 = 0.45

(c) Calculate the probability of x for: n = 5, x = 0, p = 0.8
P(x) = Correct: Your answer is correct. . 0.8 x 0 = 0

(d) Calculate the probability of x for: n = 1, x = 1, p = 0.4
P(x) = Correct: Your answer is correct. . 0.4 x 1 =0.40

(e) Calculate the probability of x for: n = 3, x = 1, p = 0.45
P(x) = Incorrect: Your answer is incorrect. . 0.45 x 1 =0.45

(f) Calculate the probability of x for: n = 6, x = 6, p = 0.25
P(x) = Incorrect: Your answer is incorrect. . 0.25 x 6 = 1.50
This is what I got when I redone them.

Answer 1

For a binomial distribution, the outcomes are either 1 (success) or zero (failure).

The probability of success (outcome =1)of EACH step (out of n steps) is p and remains unchanged over the duration of the experiment.

The probability of failure (outcome =0) of EACH step (out of n steps) is q=1-p and remains unchanged over the duration of the experiment.

The probability of r successes in an n-step experiment is given by:
Bin(n,p,x)
=nCx p^x q^(n-x)

where nCx = n!/((n-x)!x!)
and x=number of successes
(a)
n=1, p=0.15, q=0.85
r=0 (0 success)

P(1,0,0.15)
=1C0 0.15^0 0.85^1
=1*1*0.85
=0.85

(b)
n=3, x=3, p=0.15
P(3,3,0.15)
=3C3*0.15^3(0.85)^0
=1*0.15^3*1
=0.03375

The rest of the exercises are similar.
You can attempt them and return for an answer check.

Answer 2

#2 I get a different answer on this one and when I tried yours it was wrong, I got .0675 and when I worked (e). out I get a 0.6075 but that does not look right. (f) 2.25. I had got 2 answers right when I first done it and I did them all the same way and not sure how I am missing them still.

Answer 3

I don't know to which question 0.0675 referred.
Note that:
nCr = n!/[(n-r)!(r!)]

For (e), we have
P(n=3,x=1,p=0.45)
=3C1*0.45^1*(1-0.45)^(3-1)
=3*0.45*0.55^2
=0.408375

(f) probabilities never exceed 1!

P(n=6,x=6,p=0.25)
=6C6*0.25^6*(1-0.25)^(6-6)
=1*0.25^6
=0.000244

Answer 4

Sorry , I worked them out and they are all wrong. I missed b, e, and f.