1. The probability that no laptops will be sold next week is very low, as the store has an average of 3 laptops sold per week. This probability can be calculated using the Poisson distribution, which is a probability distribution used to model the number of times an event occurs within a given time period. The probability of no events occurring within a given time period is given by the formula:P(x=0) = e^(-lambda)
Where lambda is the average number of events per time period. In this case, the probability that no laptops will be sold next week is:
P(x=0) = e^(-3) = 0.0498
2. The probability that a laptop will be sold next week can also be calculated using the Poisson distribution. The probability of at least one event occurring within a given time period is given by the formula:
P(x>=1) = 1 - P(x=0) = 1 - e^(-lambda)
In this case, the probability that a laptop will be sold next week is:
P(x>=1) = 1 - e^(-3) = 0.9502
3. The probability that only one laptop will be sold tomorrow (Tuesday) can be calculated using the Poisson distribution. The probability of x events occurring within a given time period is given by the formula:
P(x) = (lambda^x * e^(-lambda)) / x!
Where lambda is the average number of events per time period and x is the number of events being considered. In this case, the probability that only one laptop will be sold tomorrow is:
P(x=1) = (3^1 * e^(-3)) / 1! = 3 * e^(-3) = 0.224
Note that this probability assumes that the store sells laptops at a constant rate throughout the week, and does not take into account any variations in demand or other factors that may affect the number of laptops sold on a given day.