at a clockmakers shop, the purchases for one month are recorded in the table below:\n| | remodel | repair |…

at a clockmakers shop, the purchases for one month are recorded in the table below:\n| | remodel | repair | new purchase |\n|--|--|--|--|\n| watch | 73 | 47 | 19 |\n| clock | 61 | 59 | 11 |\n| alarm clock | 83 | 41 | 17 |\nif we choose a customer at random, what is the probability that they have purchased a watch or a repair?\np(watch or repair) =?\ngive your answer in simplest form.

at a clockmakers shop, the purchases for one month are recorded in the table below:\n| | remodel | repair | new purchase |\n|--|--|--|--|\n| watch | 73 | 47 | 19 |\n| clock | 61 | 59 | 11 |\n| alarm clock | 83 | 41 | 17 |\nif we choose a customer at random, what is the probability that they have purchased a watch or a repair?\np(watch or repair) =?\ngive your answer in simplest form.

Answer

Explanation:

Step1: Calculate total number of purchases

First, find the sum of all values in the table. $73 + 47+19+61 + 59+11+83+41+17=411$

Step2: Calculate number of watch - related and repair - related purchases

Number of watch - related purchases: $73 + 47+19 = 139$ Number of repair - related purchases: $47+59 + 41=147$ Number of watch - and - repair purchases (overlap): $47$ Using the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, the number of watch or repair purchases is $139+147 - 47=239$

Step3: Calculate the probability

The probability $P(\text{Watch or Repair})=\frac{\text{Number of watch or repair purchases}}{\text{Total number of purchases}}=\frac{239}{411}$

Answer:

$\frac{239}{411}$