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) = Correct: Your answer is correct. . (0.85)
(b) Calculate the probability of x for: n = 3, x = 3, p = 0.15
P(x) = Incorrect: Your answer is incorrect. . (0.68)
(c) Calculate the probability of x for: n = 5, x = 0, p = 0.8
P(x) = Correct: Your answer is correct. . (0.00)
(d) Calculate the probability of x for: n = 1, x = 1, p = 0.4
P(x) = Correct: Your answer is correct. . (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)
(f) Calculate the probability of x for: n = 6, x = 6, p = 0.25
P(x) = (1.50)
I worked these all the same way got three right and three wrong can someone explain to me how???? I multiplied p to x to get answers.
What did you do for #a?
P(n=1, x=0, p=0.15)
=nPx 0.15^0((1-0.15)^(1-0)
=1!/(0!1!)(0.15^0)(0.85)^1
=1*1*0.85
=0.85
For #b,
P(n=3,x=3,p=0.15)
=3P3 (0.15^3)(1-0.15)^(3-3)
=1*(0.003375)(0.85^0)
=0.003375
Check out the other numbers using
P(n,x,p)
=nPx (p^x)(q^(n-x))
where q=(1-p)
To calculate the probability of a binomial random variable, you can use the binomial probability formula:
P(x) = (nCx) * p^x * (1-p)^(n-x)
where:
- P(x) is the probability of x,
- n is the number of trials,
- x is the number of successes,
- p is the probability of success in a single trial, and
- (nCx) represents the binomial coefficient, which is the number of ways to choose x successes out of n trials and is calculated as nCx = n! / (x! * (n-x)!)
Let's go through each question and calculate the probabilities step by step:
(a) n = 1, x = 0, p = 0.15
P(x) = (1C0) * 0.15^0 * (1-0.15)^(1-0)
= 1 * 1 * 0.85
= 0.85
(b) n = 3, x = 3, p = 0.15
P(x) = (3C3) * 0.15^3 * (1-0.15)^(3-3)
= 1 * 0.15^3 * 0.85^0
= 0.003375
(c) n = 5, x = 0, p = 0.8
P(x) = (5C0) * 0.8^0 * (1-0.8)^(5-0)
= 1 * 1 * 0.2^5
= 0.00
(d) n = 1, x = 1, p = 0.4
P(x) = (1C1) * 0.4^1 * (1-0.4)^(1-1)
= 1 * 0.4 * 1
= 0.40
(e) n = 3, x = 1, p = 0.45
P(x) = (3C1) * 0.45^1 * (1-0.45)^(3-1)
= 3 * 0.45 * 0.55^2
= 0.35685
(f) n = 6, x = 6, p = 0.25
P(x) = (6C6) * 0.25^6 * (1-0.25)^(6-6)
= 1 * 0.25^6 * 0.75^0
= 0.000244140625
It seems you made some errors in your calculations for (b) and (e). Make sure to apply the binomial probability formula correctly and double-check your calculations to get accurate results.