Smitty's Bar and Grill has brand name recognition of 61% around the world. Assuming we randomly select 2 people. The assumptions of a Bernoulli process are met. What is the probability
a)exacatly 5 of the 12 recognize the name of Smitty's Bar and Grill?
b)5 or fewer recognize Smitty's Bar and Grill
c)more than 5 recognize Smitty's Bar and Grill?
d) no one in the sample ever heard of Smitty's Bar and Grill
i think it is b) beacuase thet had only asked 2 people how can they get results by asking two people they have to ask more than 2 people to see.
I have a strong feeling that you have a typo, and that you meant to say,
"Assuming we randomly select 12 people. "
Please confirm.
if it is 12 people she meant then the answer would be c)
These are not multiple choice answers, they are individual questions
a) prob that exactly 5 out of 12 will recognize
= C(12,5)(.61)^5(.39)^7
= appr 0.0918
b)
prob = C(12,0)(.61)^0 (.39)^12 + C(12,1)(.61)^1 (.39)^11 + ... + C(12,5)(.61)^5 (.39)^7
c) prob = 1 - (answer to b)
d) prob = C(12,0)(.61)^0 (.39)^12
= .00001238
To answer these probability questions, we can use the binomial probability formula. The formula for the probability of getting exactly k successes in n trials is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
- C(n, k) is the number of combinations of n items taken k at a time.
- p is the probability of success for a single trial.
- n is the number of trials.
- k is the number of successes.
Now let's solve each probability question step by step:
a) The probability of exactly 5 people out of 12 recognizing the name of Smitty's Bar and Grill:
In this case, n = 12 (number of trials), k = 5 (number of successes), and p = 0.61 (probability of recognition).
So the probability can be calculated as:
P(X = 5) = C(12, 5) * 0.61^5 * (1 - 0.61)^(12 - 5)
You can evaluate the combination and the exponentiation, then multiply them together to get the probability.
b) The probability of 5 or fewer people recognizing Smitty's Bar and Grill:
To find this probability, we need to calculate the sum of probabilities for k = 0, 1, 2, 3, 4, and 5. So the probability is:
P(X <= 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
You can use the binomial probability formula as mentioned above and add up these probabilities.
c) The probability of more than 5 people recognizing Smitty's Bar and Grill:
To find this probability, we need to calculate the sum of probabilities for k > 5. So the probability is:
P(X > 5) = 1 - P(X <=5)
Calculate P(X <= 5) as explained in part b) and subtract it from 1.
d) The probability of no one in the sample ever hearing of Smitty's Bar and Grill:
In this case, the number of successes (k) is 0. So the probability can be calculated as:
P(X = 0) = C(12, 0) * 0.61^0 * (1 - 0.61)^(12 - 0)
Evaluate the combination and raise (1 - 0.61) to the power of 12.
By following these steps, you can find the probabilities for each scenario.