Experience shows that a ski lodge will be full (154 guests) if there is a heavy snow fall in December, while only partially full (93 guests) with a light snow fall. What is the expected number of guests if the probability for a heavy snow fall is 0.40?
same question here, just some of the numbers have changed.
https://www.jiskha.com/display.cgi?id=1263859454
Im not understanding on how you got the answer
To solve this problem, we need to calculate the expected number of guests based on the probability of a heavy snowfall.
Let's assign variables:
- Let X be the number of guests if there is a heavy snowfall.
- Let Y be the number of guests if there is a light snowfall.
- Let P(X) be the probability of a heavy snowfall.
- Let P(Y) be the probability of a light snowfall.
Given information:
- The number of guests if there is a heavy snowfall is 154 (X = 154).
- The number of guests if there is a light snowfall is 93 (Y = 93).
- The probability of a heavy snowfall is 0.40 (P(X) = 0.40).
To find the expected number of guests, we can use the following formula:
Expected number of guests = (Number of guests if X occurs) * P(X) + (Number of guests if Y occurs) * P(Y)
Let's plug in the values:
Expected number of guests = (154 * 0.40) + (93 * (1 - 0.40))
Calculating:
Expected number of guests = 61.6 + 55.8 = 117.4
Therefore, the expected number of guests, when the probability of a heavy snowfall is 0.40, is approximately 117.4 guests.