calculating probabilities

Sue0113 said:

. For a childselected at random from the population described by the table, show how tocompute the following probabilities: P(Red) 286/5387 = .05
P(Red hair and dark eyes) 286/1315 = .22
P(red hair Dark eyes) 286/1315 = .22
P(Blue and Black hair) 718/5387 = .13 Are 4 equations and these correct?

Eyes Fair Red Med Dark Black TOTAL
Blue 326 38 241 110 3 718
Light 688 116 584 188 4 1580
Med 343 84 909 412 26 1774
Dark 98 48 403 681 85 1315
TOTAL 1455 286 2137 1391 118 5387

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The first is correct, but the others are not correct as typed.

The probability that both "Red Hair" and "Dark Eyes" are true, within the total population, is
P(Red Hair & Dark Eyes) = 48/5387

But did the problem ask that question twice? or was one question "Given Dark Eyes, what is the probability of Red Hair?" In that case you would compare the number with both traits (48) to the total number with Dark Eyes (1315). That can be written as a conditional probability, which may be written with a vertical bar, "|".
P(Red Hair | Dark Eyes) = 48/1315

You have said there are 718 people with both blue eyes and black hair .. but in the table there are only 3 people in that box.

If you want to try some additional problems, consider these:
What is the probability of Black Hair?
What is the probability of Medium Eyes?
What is the probability of both Black Hair and Medium Eyes?
Given Black Hair, what is the probability of Medium Eyes?
Given Medium Eyes, what is the probability of Black Hair?