Question

use the information provided to answer part a and part b for question 19.

1. the two - way table shows the classification of students in a mathematics class by gender and dominant hand. a student who is ambidextrous uses both hands equally well.

	male	female	total
left - handed	4	2	6
ambidextrous	1	0	1
total	16	14	30

part a
what is the probability that a randomly selected student in the class is female given that the student is right - handed?
a. \\(\frac{1}{12}\\)
b. \\(\frac{12}{30}\\)
c. \\(\frac{12}{23}\\)
d. \\(\frac{23}{30}\\)

Explanation:

Step1: Calculate the total number of students

The total number of students is \(16 + 14=30\) (from the "Total" row in the table).

Step2: Calculate the number of right - handed students

The number of right - handed students is \(11 + 12=23\) (sum of male and female right - handed students).

Step3: Use the probability formula

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of favorable outcomes and \(n(S)\) is the total number of outcomes. Here, \(n(A) = 23\) (right - handed students) and \(n(S)=30\) (total students). So the probability \(P=\frac{23}{30}\)

Answer:

D. \(\frac{23}{30}\)