In a survey of 204 people, the following incomplete information was recorded relating gender to color-blindness:
Complete the table on a separate sheet of paper, then complete Parts (a) - (d). There are no required fill-ins within the table.
Color-Blind Not Color-Blind Total
Male ________ ________ 134
Female ________ 27 70
Total 115 89 204
Parts (a) - (d) deal with probability using the table. It is best to enter answers as fractions rather than decimals. It precludes the problems of rounding. Otherwise enter at least 6 decimal places.
A person is randomly selected. What is the probability that the person is:
(a) Female?
(b) Male or Color-blind?
(c) Female given that the person is not Color-blind?
(d) Color-blind given that the person is Male?
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To answer these probability questions, we need to use the information provided in the table. Let's go through each part and calculate the probabilities.
(a) To find the probability that a randomly selected person is female, we need to find the ratio of the number of females to the total number of people.
From the table, we see that there are 70 females out of a total of 204 people. So the probability of selecting a female person is:
Probability (female) = Number of females / Total number of people
= 70 / 204
(b) To find the probability that a randomly selected person is male or color-blind, we need to sum up the number of males and the number of color-blind individuals and divide it by the total number of people.
Let's fill in the missing values in the table. We know that the total number of males is 134, and the total number of color-blind people is 115.
To calculate the probability of a person being male or color-blind, add the number of males and color-blind individuals, then divide it by the total number of people:
Probability (male or color-blind) = (Number of males + Number of color-blind individuals) / Total number of people
= (134 + 115) / 204
(c) To find the probability that a randomly selected person is female given that they are not color-blind, we need to consider only the subset of people who are not color-blind.
From the table, we know that there are 89 people who are not color-blind. Out of these 89 people, 27 are female.
To calculate the probability of a person being female given that they are not color-blind, divide the number of females who are not color-blind by the total number of people who are not color-blind:
Probability (female | not color-blind) = Number of females who are not color-blind / Total number of people who are not color-blind
= 27 / 89
(d) To find the probability that a randomly selected person is color-blind given that they are male, we need to consider only the subset of males.
From the table, we know that there are 134 males in total. And out of these 134 males, 115 are color-blind.
To calculate the probability of a person being color-blind given that they are male, divide the number of color-blind males by the total number of males:
Probability (color-blind | male) = Number of color-blind males / Total number of males
= 115 / 134
You can now substitute the values into the formulas to find the probabilities for each part of the question. Remember to express probabilities as fractions or decimals if needed.