Question

you pick a card at random. what is p(odd or greater than 1)? write your answer as a fraction or whole number.

Explanation:

Step1: Calculate the number of odd - numbered cards

The odd - numbered cards are \(1\), \(3\), \(5\), \(7\). So \(n(\text{odd}) = 4\).

Step2: Calculate the number of cards greater than \(1\)

The cards greater than \(1\) are \(2\), \(3\), \(4\), \(5\), \(6\), \(7\), \(8\). So \(n(\text{greater than }1)=7\).

Step3: Calculate the number of cards that are odd and greater than \(1\)

The cards that are odd and greater than \(1\) are \(3\), \(5\), \(7\). So \(n(\text{odd and greater than }1) = 3\).

Step4: Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

By the formula \(P(\text{odd or greater than }1)=\frac{n(\text{odd})+n(\text{greater than }1)-n(\text{odd and greater than }1)}{n(\text{total})}\). The total number of cards \(n(\text{total}) = 8\).
Substitute the values: \(\frac{4 + 7-3}{8}=\frac{8}{8}\)

Answer:

\(1\)