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**somestudent2** A heavy equipment sales person can contact either one or two customers per day with probability 1/3 and 2/3 respectively. Each contact will result in no sale or a $50 000 sale with the probabilities .9 and .1. Give the probability distribution for daily sales. Find the mean and standard deviation of the daily sales.

Here is how I started:

Let Y denote # of daily sales. Then Range of Y = {0,1,2}

Given: P(contacting 1) = 1/3

P(contacting 2) = 2/3

P(Sale) = 1/10

P(No Sale) = 9/10

Possible outcomes:

Contacted 1 sold 0

Contacted 1 sold 1

Contacted 2 sold 0

Contacted 2 sold 1

Contacted 2 sold 2

Now I have a problem in going further, how do I calculate these probabilities to create distribution of Y. For example how to calculate contacted 2 sold 1 or contacted 2 sold 2? Are the events independent?

Should it be something like this

P of SS(Sale Sale) 1/10 * 1/10 = 1/100

P of SN(Sale no Sale) 1/10*9/10= 9/100

P of NN(no sale no sale) 9/10 *9/10 = 81/100

then use these values to calculate:

P(Y= 0)= 1/3 * 81/100 + 2/3 * 81/100 = 81/100

P(Y = 1) = 1/3 * 9/100 + 2/3 * 9/100 = 9/100

P(Y = 2) = 2/3 * 1/100 + 1/3 * 1/100 = 1/100

?