Answer to Question #302071 in Discrete Mathematics for BxJ

Question

Mark is shopping for a new mobile phone. The

probability that someone buys Oppo is 25%,

Huawei is 20%, Vivo is 10%, both Oppo and

Vivo is 5%, both Oppo and Huawei is 7%,

both Vivo and Huawei is 3%, and of the three

brands is 2%. What is the probability that

Mark buys Oppo or Huawei?

Answer 1

Let $O$ denote the event "buy Oppo", $H$ denote the event "buy Huawei,"

$V$ denote the event "buy Vivo".

$$P(O)=0.25, P(H)=0.20, P(V)=0.10$$

$$P(O\cap V)=0.05, P(O\cap H)=0.07,$$

$$P(H\cap V)=0.03,P(O\cap H\cap V)=0.02$$

The probability that Mark buys Oppo or Huawei is

$$P(O\cup H)=P(O)+P(H)-P(O\cap H)$$

$$=0.25+0.20-0.07=0.38$$