Need major help on this one. Sooo confused...
Binomial distribution to solve the problems. There is a 60 percent probability that a store will sell one of Red bags to any customer who comes into the shop and views the bags. Out of the next 7 people who come into the shop, what is the probability that 3 people will buy a bag? What is the probability that more than four people will buy the bag?
The probability of three purchases after seven customer visits is
P(3) = (0.6)^3*(0.4)^4*C(7,3)
where C(7,3) is the binomial coefficient
C(7,3) = 7!/(4!*3!) = 70
I get 0.387 for the answer.
For P(n>4), add P(5), P(6) and P(7)
For an explanation of how the probability relates to the binomial coefficient, see
http://en.wikipedia.org/wiki/Binomial_coefficient
How do you get 70. When I calculate the formula I get 35.
7!/(4!*3!) = 5*6*7/(1*2*3)= 210/6 = 35
You are right
To solve this problem, we can use the binomial distribution formula. The formula for the probability of getting exactly x successes in n trials, given a probability p of success in each trial, is:
P(X = x) = C(n, x) * p^x * (1-p)^(n-x)
Where:
- P(X = x) is the probability of getting exactly x successes,
- C(n, x) is the number of combinations of n items taken x at a time, calculated as n! / (x! * (n-x)!),
- p is the probability of success in each trial,
- x is the number of successes,
- n is the total number of trials.
In this case, the probability of a customer buying a Red bag is 60%, or 0.6. Therefore, p = 0.6. We want to find the probability of 3 people buying a bag out of the next 7 people, so x = 3 and n = 7.
To find the probability that exactly 3 people will buy a bag, we can substitute these values into the formula and calculate:
P(X = 3) = C(7, 3) * 0.6^3 * (1-0.6)^(7-3)
P(X = 3) = 35 * 0.6^3 * 0.4^4
P(X = 3) = 35 * 0.216 * 0.0256
P(X = 3) ≈ 0.0403
Therefore, the probability that exactly 3 people will buy a bag out of the next 7 people is approximately 0.0403.
To find the probability that more than four people will buy the bag, we need to calculate the probability of having 5, 6, or 7 people buying a bag. We can then add these probabilities together.
P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7)
Using the same formula, we can calculate each probability:
P(X = 5) = C(7, 5) * 0.6^5 * 0.4^2
P(X = 6) = C(7, 6) * 0.6^6 * 0.4^1
P(X = 7) = C(7, 7) * 0.6^7 * 0.4^0
By substituting the values and calculating each probability, we can find the total probability:
P(X > 4) = 0.2321 + 0.1858 + 0.0983
P(X > 4) ≈ 0.5162
Therefore, the probability that more than four people will buy the bag out of the next 7 people is approximately 0.5162.