determine the following proportion.\nthe following table categorizes the students in a first - grade class…

determine the following proportion.\nthe following table categorizes the students in a first - grade class by age and gender.\n| | age | | | |\n|--|--|--|--|--| \n| gender | 5 years old | 6 years old | 7 years old | totals |\n| male | 2 | 9 | 1 | 12 |\n| female | 2 | 6 | 0 | 8 |\n| totals | 4 | 15 | 1 | 20 |\nwhat proportion of the students are female or less than 6 years old?\n10/20\n12/20\n2/20\n4/20\n8/20

determine the following proportion.\nthe following table categorizes the students in a first - grade class by age and gender.\n| | age | | | |\n|--|--|--|--|--| \n| gender | 5 years old | 6 years old | 7 years old | totals |\n| male | 2 | 9 | 1 | 12 |\n| female | 2 | 6 | 0 | 8 |\n| totals | 4 | 15 | 1 | 20 |\nwhat proportion of the students are female or less than 6 years old?\n10/20\n12/20\n2/20\n4/20\n8/20

Answer

Explanation:

Step1: Find number of female students

There are 8 female students as shown in the total - female row.

Step2: Find number of students less than 6 years old

There are 4 students who are 5 years old.

Step3: Find number of female students who are less than 6 years old

There are 2 female students who are 5 years old.

Step4: Use the formula for (P(A\cup B))

The formula for (P(A\cup B)=P(A)+P(B)-P(A\cap B)). Here, (A) is the event of being female and (B) is the event of being less - than 6 years old. The number of students who are female or less than 6 years old is (8 + 4-2=10).

Step5: Calculate the proportion

The total number of students is 20. So the proportion is (\frac{10}{20}).

Answer:

10/20