The probability of shopping as Shoprite supermarket is 60% while that of shopping at Pick and Pay is 40%. If the shopper goes shopping eight times.
A. what is the probability of Shopping at least three times at Shoprite supermarket.
B. Shopping at most three times at Pick and Pay supermarket.
C. Shopping at one supermarket.
I just need an insight as to whether this binomial probability or not
binomial probability
To find the probability of shopping at least three times at Shoprite supermarket, we can use the concept of binomial probability. The formula for binomial probability is:
P(X = k) = (nCk) * (p^k) * ((1 - p)^(n - k))
Where:
- P(X = k) is the probability of getting exactly k successes.
- n is the number of trials.
- k is the number of desired successes.
- p is the probability of success in each trial.
- (nCk) is the combination, representing the number of ways to choose k successes from n trials.
Let's calculate the probabilities for the given scenarios.
A. Probability of Shopping at least three times at Shoprite supermarket:
P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)
In this case, n = 8 (number of trials) and p = 0.6 (probability of shopping at Shoprite).
P(X = 3) = (8C3) * (0.6^3) * (0.4^5)
P(X = 4) = (8C4) * (0.6^4) * (0.4^4)
P(X = 5) = (8C5) * (0.6^5) * (0.4^3)
P(X = 6) = (8C6) * (0.6^6) * (0.4^2)
P(X = 7) = (8C7) * (0.6^7) * (0.4^1)
P(X = 8) = (8C8) * (0.6^8) * (0.4^0)
Calculate each term and sum them up to find P(X ≥ 3).
B. Probability of Shopping at most three times at Pick and Pay supermarket:
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
In this case, n = 8 (number of trials) and p = 0.4 (probability of shopping at Pick and Pay).
P(X = 0) = (8C0) * (0.4^0) * (0.6^8)
P(X = 1) = (8C1) * (0.4^1) * (0.6^7)
P(X = 2) = (8C2) * (0.4^2) * (0.6^6)
P(X = 3) = (8C3) * (0.4^3) * (0.6^5)
Calculate each term and sum them up to find P(X ≤ 3).
C. Probability of Shopping at one supermarket:
P(One Supermarket) = P(X = 8) + P(X = 0)
In this case, n = 8 (number of trials) and p = 0.6 (probability of shopping at Shoprite) or p = 0.4 (probability of shopping at Pick and Pay).
P(X = 8) = (8C8) * (0.6^8) * (0.4^0)
P(X = 0) = (8C0) * (0.6^0) * (0.4^8)
Calculate each term and sum them up to find P(One Supermarket).
Using these calculations, we can find the desired probabilities.