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A salesman has scheduled two appointments to sell vacuum cleaners. His first appointment will lead to a sale with probability .3, and his second will lead independently to a sale with probability .6. Any sale made is equally likely to be either for the deluxe model, which costs $1000, or the standard model, which costs $500. Determine the probability mass function of , the total dollar value of all sale

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The probable total dollar value of all sale is $ 675.

Given that a salesman has scheduled two appointments to sell vacuum cleaners, and his first appointment will lead to a sale with probability 0.3, and his second will lead independently to a sale with probability 0.6, and any sale made is equally likely to be either for the deluxe model, which costs $ 1000, or the standard model, which costs $ 500, to determine the probability mass function of the total dollar value of all sale, the following calculation must be performed:

  • 0.3 / 2 = 0.15
  • 0.6 / 2 = 0.3
  • 1000 x 0.15 + 1000 x 0.3 + 500 x 0.15 + 500 x 0.3 = X
  • 150 + 300 + 75 + 150 = X
  • 675 = X

Therefore, the probable total dollar value of all sale is $ 675.

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