Thirty-three percent of workers in a city are college graduates. If you randomly select 20 workers...
(A) what is the probability that five or six of them are college graduates?
(b) what is the probability that more than 2 are college graduates ?
Can someone please help I am struggling
Prob(graduate) = .33
prob(not grad) = .67
prob(probability that five or six of the 20 are grads)
= C(20,5)(.33)^5 (.67)^15 + C(20,6) (.33)^6 (.67)^14
= ..... you do the button pushing stuff
prob(of 20 that more than 2 are grads)
= prob(3 are grads) + prob(4 are grads) + ...+ prob(20 are grads)
too much work, so
prob(of 20 that more than 2 are grads)
= 1 - (prob(0 grads) + prob(1 is a grad) + prob( 2 are grads)
this way you only have 3 calculations
= .....
Sure! I'd be happy to help you with these probability questions.
To solve these problems, we can use the binomial probability formula, which is given by:
P(x) = (nCx)(p^x)((1-p)^(n-x))
Where:
P(x) represents the probability of x successes,
nCx represents the number of combinations of n items taken x at a time,
p represents the probability of success for one trial,
n represents the total number of trials, and
x represents the number of successful trials we are interested in.
Now let's solve the problems step by step:
(A) What is the probability that five or six of them are college graduates?
Step 1: Calculate the probability of success (p). In this case, p is the probability that one worker is a college graduate, which is given as 33% or 0.33.
Step 2: Calculate the number of trials (n). Here, we are randomly selecting 20 workers.
Step 3: Calculate the probability of getting exactly five college graduates by substituting the values into the binomial probability formula:
P(5 college graduates) = (20C5)(0.33^5)((1-0.33)^(20-5))
Step 4: Calculate the probability of getting exactly six college graduates using the same process:
P(6 college graduates) = (20C6)(0.33^6)((1-0.33)^(20-6))
Step 5: Calculate the total probability of getting either five or six college graduates by summing the two probabilities calculated in step 3 and step 4.
P(five or six college graduates) = P(5 college graduates) + P(6 college graduates)
(B) What is the probability that more than 2 are college graduates?
Step 1: Calculate the probability of success (p) as before: 0.33.
Step 2: Calculate the number of trials (n): 20.
Step 3: Calculate the probability of getting 0, 1, or 2 college graduates and subtract that probability from 1 to get the probability of more than 2 college graduates:
P(more than 2 college graduates) = 1 - [P(0 college graduates) + P(1 college graduate) + P(2 college graduates)]
To calculate the probabilities of 0, 1, or 2 college graduates, substitute the values into the binomial probability formula as we did in step 3 for (A).
I hope this helps! Let me know if you have any further questions.