Question

the probability a student owns a tablet computer (like an ipad) is 0.25. the probability a student owns a smart phone is 0.7, and 20% of students own both. what’s the chance if we select a student at random, that he or she owns neither of these? enter your answer as a decimal, not as a percent.

Explanation:

Step1: Define Events

Let \( T \) be the event that a student owns a tablet, \( P(T) = 0.25 \). Let \( S \) be the event that a student owns a smartphone, \( P(S) = 0.7 \). The probability that a student owns both is \( P(T \cap S) = 0.2 \) (since 20% = 0.2).

Step2: Use Inclusion - Exclusion Principle

The probability of \( T \) or \( S \) is \( P(T \cup S)=P(T)+P(S)-P(T \cap S) \).
Substitute the values: \( P(T \cup S)=0.25 + 0.7-0.2 \).
First, \( 0.25+0.7 = 0.95 \), then \( 0.95 - 0.2=0.75 \).

Step3: Probability of Neither

The probability of neither \( T \) nor \( S \) is \( 1 - P(T \cup S) \).
Substitute \( P(T \cup S) = 0.75 \): \( 1 - 0.75 = 0.25 \).

Answer:

\( 0.25 \)