Question

example 3: suppose a class contains 60 students, and some students participate on the soccer team and some on the debate team. 10 students only participate in debate, 31 students participate only on the soccer team, and 12 students participate in both.(hint: a key word here is the word \only\)a.) what is the probability that a student participates on the soccer team?b.) what is the probability that a student participates on the debate team?c.) what is the probability that a student participates on either the soccer team or on the debate team?d.) what is the probability that a student participates neither on the soccer team nor on the debate team?

Explanation:

Step1: Calculate total soccer participants

Soccer participants = Only soccer + Both = $31 + 12 = 43$

Step2: Find soccer team probability

Probability = $\frac{\text{Total soccer}}{\text{Total students}} = \frac{43}{60}$

Step3: Calculate total debate participants

Debate participants = Only debate + Both = $10 + 12 = 22$

Step4: Find debate team probability

Probability = $\frac{\text{Total debate}}{\text{Total students}} = \frac{22}{60} = \frac{11}{30}$

Step5: Calculate either team participants

Either team = Only soccer + Only debate + Both = $31 + 10 + 12 = 53$

Step6: Find either team probability

Probability = $\frac{\text{Either team}}{\text{Total students}} = \frac{53}{60}$

Step7: Calculate neither team participants

Neither team = Total students - Either team = $60 - 53 = 7$

Step8: Find neither team probability

Probability = $\frac{\text{Neither team}}{\text{Total students}} = \frac{7}{60}$

Answer:

a.) $\frac{43}{60}$
b.) $\frac{11}{30}$
c.) $\frac{53}{60}$
d.) $\frac{7}{60}$