A person visits three friends. He found that his wallet was lost when he comes back. The probabilities that his wallet will be lost at each friends’ home are 0.4, 0.2, and 0.1, respectively, in the order of visiting. Given that his wallet was lost at one of his three friend’s homes, what is the probability that his wallet was left at the first friend’s home? Hint: Define W = the wallet was lost at one of the three homes, Ai = the wallet was lost at the ith friend’s home, i=1, 2, 3. The Question gives P(A1)=0.4, P(A2|A1c)=0.2, P(A3|(A1cintersectionA2c))=0.1, and we want to calculate P(A1|W). You can find P(W) by either working on its complement or summing up the probability that all Ai occurs.

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24