Question

Gender and Handedness. This problem requires that you first obtain the gender and handedness of each student in your class. Subsequently, determine the probability that a randomly selected student in your class is

(a). female.

(b) left-handed.

(c) female and left-handed.

(d) neither female nor left-handed.

Short answer

Part (a) 0.3.

Part (b) 0.34.

Part (c) 0.09.

Part (d) 0.45.

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

This problem requires that you first obtain the gender and handedness of each student in your class.

Assume there are 100 pupils in the class, with 9 left-handed females, 21 right-handed females, 25 left-handed males, and 45 right-handed males.

Part (a) Step 2. Find the probability that the selected student is a female.

The likelihood that a randomly chosen student is female. Females who are both left and right-handed have favorable outcomes. in this case or we can say that all females will be considered here.

Then the favorable outcomes will become: $9+21=30$

The total number of outcomes: 100

The probability that a female is selected is:

$$\begin{gathered} P\left(E\right)=\frac{30}{100} \\ =0.3 \end{gathered}$$

Part (b) Step 1. Find the probability that the selected student is left-handed.

The likelihood that a randomly chosen student is left-handed.

Total left-handed students include: $9+25=34$

Then the favorable outcomes will become 34.

The probability that a left-handed is selected is:

$$\begin{gathered} P\left(E\right)=\frac{34}{100} \\ =0.34 \end{gathered}$$

Part (c) Step 1. Find the probability that the selected student is female and left-handed.

The likelihood that a randomly chosen student is female and left-handed.

Then the favorable outcomes will become: 9

The probability that a female and left-handed is selected is:

$$\begin{gathered} P\left(E\right)=\frac{9}{100} \\ =0.09 \end{gathered}$$

Part (a) Step 2. Find the probability that the selected student is neither female nor left-handed.

The likelihood that a randomly chosen student is neither female nor left-handed.

in this case, all right-handed will be considered.

Then the favorable outcomes will become: 45

The probability that a left-handed is selected is:

$$\begin{gathered} P\left(E\right)=\frac{45}{100} \\ =0.45 \end{gathered}$$