Question

A survey of 100 people in New York City, NY found that.

• The probability that they take the subway each day is 0.85
• The probability that they take a Taxi each day is 0.6
• The probability that take the subway and taxi each day is 0.55

If a person is selected at random, then determine the probability thay they take either the subway or a taxi each day.

Answer 1

Answer: 0.9

Explanation:

`\mathrm{Total \ sample \ space \ $=100$} \\\mathrm{Event \ $A = \ taking \ subway \ each \ day}$$P(A)=0.85$$Event $B=$ taking taxi $\because P(B)=0.6$$$P(A \cap B)=0.55$$`

`\begin{aligned}P(A \cup B) & \Rightarrow \text { Person taking either taxi/subway } \\&=P(A)+P(B)-P(A \cap B) \\&=(0.85-0.555)+(0.6-0.55)-0.55 \\&=1.45-0.55\\&\bf{=0.9} \end{aligned}`