2.3 Exercise 19

A computer store sells computers, monitors, printers. A customer enters the store. Let A, B, C be the respective events the customer buys a computer, a monitor, a printer. Assume the following probabilities:

1. $$ The probability $P \left(A B\right)$ of buying both a computer and a monitor is 0.49.
2. $$ The probability $P \left(A B C^{c}\right)$ of buying both a computer and a monitor but not a printer is 0.17.
3. $$ The probability $P \left(A C\right)$ of buying both a computer and a printer is 0.45.
4. $$ The probability $P \left(B C\right)$ of buying both a monitor and a printer is 0.39
5. $$ The probability $P \left(A C^{c} \vee A^{c} C\right)$ of buying a computer or a printer, but not both is 0.50.
6. $$ The probability $P \left(A B^{c} \vee A^{c} B\right)$ of buying a computer or a monitor, but not both is 0.43.
7. $$ The probability $P \left(B C^{c} \vee B^{c} C\right)$ of buying a monitor or a printer, but not both is 0.43.

1. What is the probability $P \left(A\right)$, $P \left(B\right)$, or $P \left(C\right)$ of buying each?
2. What is the probability of buying exactly two of the three items?
3. What is the probability of buying at least two?
4. What is the probability of buying all three?