Question

The two way frequency table shows the results of a survey of middle school students. Find the probability that a randomly chosen student is a male who enjoys reading.

Answer 1

the two way Frequency table is also required

Answer 2

The probability that a randomly chosen student is a male who enjoys reading = 0.13 (Rounded to nearest thousandth)

Correct question : The two way frequency table shows the results of a survey of middle school students. Find the probability that a randomly chosen student is a male who enjoys reading. Round to the nearest thousandth

$\begin{array}{ | c | c|c |c | } \hline \\ \bf Enjoys \:Reading & \bf \: Yes & \bf No & \bf \:Totals \\ \hline \\ \bf Female\:& \sf 40& \sf30& \sf 70 \\ \hline \\ \bf Male \:& \sf 15& \sf 30& \sf 45 \\ \hline \\ \bf Totals\:& \sf 55& \sf 60& \sf 115 \\ \hline\end{array}$

Given :

The two way frequency table shows the results of a survey of middle school students.

$\begin{array}{ | c | c|c |c | } \hline \\ \bf Enjoys \:Reading & \bf \: Yes & \bf No & \bf \:Totals \\ \hline \\ \bf Female\:& \sf 40& \sf30& \sf 70 \\ \hline \\ \bf Male \:& \sf 15& \sf 30& \sf 45 \\ \hline \\ \bf Totals\:& \sf 55& \sf 60& \sf 115 \\ \hline\end{array}$

To find :

The probability that a randomly chosen student is a male who enjoys reading. Round to the nearest thousandth

Solution :

Step 1 of 3 :

Find total number of possible outcomes

Here the given frequency table of the survey of middle school students

$\begin{array}{ | c | c|c |c | } \hline \\ \bf Enjoys \:Reading & \bf \: Yes & \bf No & \bf \:Totals \\ \hline \\ \bf Female\:& \sf 40& \sf30& \sf 70 \\ \hline \\ \bf Male \:& \sf 15& \sf 30& \sf 45 \\ \hline \\ \bf Totals\:& \sf 55& \sf 60& \sf 115 \\ \hline\end{array}$

Total number of students in the school = 115

So total number of possible outcomes = 115

Step 2 of 3 :

Find total number of possible outcomes for the event

Let A be the event that a randomly chosen student is a male who enjoys reading

Number of student who is a male and enjoys reading = 15

So total number of possible outcomes for the event A is 15

Step 3 of 3 :

Find the probability of the event

The probability of the event

= The probability that a randomly chosen student is a male who enjoys reading.

= P(A)

$\displaystyle \sf{ = \frac{Number \: of \: favourable \: cases \: to \: the \: event \: A }{Total \: number \: of \: possible \: outcomes }}$

$\displaystyle \sf = \frac{15}{115}$

$\displaystyle \sf = 0.130434783$

Now the digit at the ten thousandths place is 4 which is less than 5

So leave the digit at the thousandths place unchanged and remove all the digits to its right.

So rounding 0.130434783 to nearest thousandth we get 0.130 which is same as 0.13

Hence the probability that a randomly chosen student is a male who enjoys reading = 0.13

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