A bookstore is promoting two books, one costing $500, and theanother with a cost of $1000. Each time a customer enters, it is offered on two separate occasions buying a book. The customer buys a book in the first offer with probability 0.3, and one in the second with probability 0.6.Let X be the random variable that measures the total amount of a customer's purchase, build the mass function probability of X.

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A bookstore is promoting two books, one costing $500, and theanother with a cost of $1000. Each time a customer enters, it is offered on two separate occasions buying a book. The customer buys a book in the first offer with probability 0.3, and one in the second with probability 0.6.Let X be the random variable that measures the total amount of a customer&#039;s purchase, build the mass function probability of X.

alenahelenash · Accepted Answer

Let&#039;s solve the given problem step by step:Given that there are two offers to buy a book each time a customer enters the store. The probability of buying a book in the first offer is 0.3 and the probability of buying a book in the second offer is 0.6.To find the probability that a customer buys a book:We can use the Law of Total Probability. It states that the total probability of an event can be found by summing up the individual probabilities of the event happening under different conditions.Let&#039;s denote the event of buying a book as B, and the events of accepting or rejecting the offers as A1 and A2 respectively. Then, we can write:P(B) = P(B|A1)P(A1) + P(B|A2)P(A2)where,P(B|A1) is the probability of buying a book given that it is offered in the first offer.P(A1) is the probability of accepting the offer in the first offer, which is 0.3 in this case.P(B|A2) is the probability of buying a book given that it is offered in the second offer.P(A2) is the probability of accepting the offer in the second offer, which is 0.6 in this case.Substituting the values, we get:P(B) = 0.3 x 0.3 + 0.6 x 0.6= 0.09 + 0.36= 0.45Therefore, the probability that a customer buys a book is 0.45 or 45%.

A bookstore is promoting two books, one costing

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