Question

learning goals from lesson 5.3
✓ i can make two - way tables, and i can find relative conditional relative frequencies. (standards: s.cp.4, s.cp.5, s.md.7+)
lesson reflection (circle one)
starting... getting there... got it!
9.
the table shows the distribution of male and female students and left - and right - handed students in the math club. find the probability that a left - handed student selected at random is female. express your answer as a fraction in simplest form.

	left - handed	right - handed
female	5	32

a. \\(\frac{5}{37}\\)

b. \\(\frac{5}{9}\\)

c. \\(\frac{5}{79}\\)

d. \\(\frac{5}{4}\\)

Explanation:

Step1: Identify left - handed students

First, we need to find the total number of left - handed students. From the two - way table, the number of left - handed male students is 4 and the number of left - handed female students is 5. So the total number of left - handed students is \(4 + 5=9\).

Step2: Identify left - handed female students

The number of left - handed female students is 5 (from the table: Female row and Left - handed column).

Step3: Calculate the probability

The probability that a left - handed student is female is the number of left - handed female students divided by the total number of left - handed students. So the probability \(P=\frac{\text{Number of left - handed female students}}{\text{Total number of left - handed students}}=\frac{5}{9}\).

Answer:

b. \(\frac{5}{9}\)