Our department store is having a sale on personal computers, of which three are

Question

Our department store is having a sale on personal computers, of which three are in stock (no rain checks). There is a certain probability of selling none. The probability of selling one is twice as great the probability of selling none. The probability of selling two is three times the probability of selling none. Finally, the probability of selling all the personal computers is four times as great the probability of selling 2 personal computers? hint-let the probability of selling none equal x.
a 0.24
b 0.27
c 0.3
d 0.33

Explanation / Answer

Let probability of selling none be x.

Probability of selling 0 = x

Probability of selling 1 = 2x

Probability of selling 2 = 3x

Probability of selling 3 = 12x

x + 2x + 3x + 12x = 1

solving, the above equation for x = 0.055

Probability of selling 0 = x = 0.055

Probability of selling 1 = 2x = 0.111

Probability of selling 2 = 3x = 0.167

Probability of selling 3 = 12x = 0.667

Expected number of computer that can be sold = 0*0.055 + 1*0.111 + 2*0.167 + 3*0.667 = 2.446

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