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Experience shows that a ski lodge will be full (161 guests) if there is a heavy snow fall in December, while only partially full (60 guests) with a light snow fall. What is the expected number of guests if the probability for a heavy snow fall is .40? Assume that heavy snow fall and light snow fall are the only two possibilities.

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Answer:

Expected number of guests is 100.4.

Step-by-step explanation:

It is given that there are 161 guest if there is a heavy snow fall.

Also, the probability for a heavy snow fall is 0.40.

Therefore, P(X = 161) =0.4.

It is also given that there are 60 guests if there is a light snow fall.

The probability for a light snow fall is 1 - 0.4 = 0.6.

Therefore, P(X = 60) = 0.6.

Expected number of guests = (161)P(X = 161) + (60)P(X = 60)

= 161(0.4) + 60(0.6)

= 64.4 + 36

= 100.4

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