<span>In the question "Based on the data in the two-way table, what is the probability that a person weighs 120 pounds, given that he or she consumes 2,000 to 2,500 calories per day?"
The probability of an event, say A given another event, say B is given by n(A and B) / n(B).
Thus the probability that a person weighs 120 pounds, given that he or she consumes 2,000 to 2,500 calories per day is given by number of persons that weigh 120 pounds and consume 2,000 to 2,500 calories per day / number of persons that consume 2,000 to 2,500 calories per day.
From the table, the number of persons that weigh 120 pounds and consume 2,000 to 2,500 calories per day is 10 while the number of persons that consume 2,000 to 2,500 calories per day is 110.
Therefore, the required probability is 10 / 110 = 1 / 11</span>
where the letter D is the diagonal matrix with diagonal entries λ1,…,λn. Now let's assume V is invertible, that is, this particular given eigenvectors are linearly independent, you get M=VDV−1.
Kindly check the attached image below to see the step by step explanation to the question above.
