Question

A man wants to buy tablets for this 2 daughter as Christmas gift. He goes to an electronics shop that has the two latest models. The probability that Sabrina, the older daughter, will accept the gift is 0.9, whereas the probability that Samantha, the younger daughter, will accept the gift is 0.7. These two probabilities are independent. There is a 0.8 probability that Sabrina will choose the first model, which cost $600, and a 0.2 probability that she chooses the second model, which cost $450. Samantha is equally likely to opt for either model. Determine the expected total cost that will incurred by the man

Answer 1

Price of Model 1 & Model 2 is $600 & $450 respectively.

The probability that Sabrina will accept Model 1 & Model 2 is 0.8 & 0.2 respectively. The expected cost of Sabrina's gift is, therefore given by:

Samantha can accept Model 1 & Model 2 equally likely. Hence, the probability of choosing each model is 0.5. The expected cost of Samantha's gift is, therefore given by:

Thus, the expected total cost for the gift of Sabrina and Samantha is $570 & $525.

It is given that Sabrina & Samantha will accept the gifts with a probability of 0.9 and 0.7 respectively.

Thus , the final expected cost is:

Hence, on average, the man will spend $880.5 on buying gifts for his daughter's.