Question

Students attending an international event were asked if they can speak Arabic or Chinese. 25% speak Arabic, 20% speak Chinese, 10% speak both languages. Phrase each of the following in terms of the events, A: Arabic and C: Chinese (using Complement, Intersection, Union). Assume random selection of one student: a. What is the probability that the student can speak Chinese or Arabic? b. What is the probability that the student cannot speak either Chinese or Arabic?

Answer 1

Answer: a) 35%, b) 65%.

Step-by-step explanation:

Since we have given that

Probability of students speak Arabic = 0.25

Probability of students speak Chinese = 0.20

Probability of students speak both language = 0.10

Let A be the event for Arabic.

Let C be the event for Chinese.

a. What is the probability that the student can speak Chinese or Arabic?

$P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\P(A\cup B)=0.25+0.20-0.10\\\\P(A\cup B)=0.35=35\%$

b. What is the probability that the student cannot speak either Chinese or Arabic?

$P(A\cup B)'=100-35=65\%$

Hence, a) 35%, b) 65%.