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.

Question

Mathematics

Karli Ramos

20 January, 19:34

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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Ivy Cooke · Answer 1

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