Experience shows that a ski lodge will be full ( 156 guests) if there is a heavy snow fall in December, while only partially full ( 57 guests) with a light snow fall. What is the expected number of guests if the probability for a heavy snow fall is .40?
If someone could please explain to me how to do this, I would greatly appreciate it. I have several problems that are just like this, and if someone can teach me how to do this, then I will know how to do the other ones.
Expected value = 156 x (probability of snow) + 57 x (probability of no snow)
Although there either will or will not be show, and the number of guests will closer to either 156 or 57, the "expected value" is the average over many similar situations.
When gambling, as in business, it is usually best to assume the expected value will occur.
To find the expected number of guests, you need to calculate the weighted average of the number of guests for each possible outcome. In this case, there are two outcomes: heavy snowfall and light snowfall.
Let's define:
- N1 as the number of guests when there is heavy snowfall (156 guests).
- N2 as the number of guests when there is light snowfall (57 guests).
- P1 as the probability of heavy snowfall (0.40).
- P2 as the probability of light snowfall (1 - P1 = 0.60).
The formula for calculating the expected number of guests (E) is:
E = N1 * P1 + N2 * P2
Now, let's plug in the values:
E = 156 * 0.40 + 57 * 0.60
Calculating this expression will give you the expected number of guests.