Question

a box contains three red playing cards numbered one to three. the box also contains five black playing cards numbered one to five. you randomly pick a playing card. it is black or has an odd number

Explanation:

Step1: Calculate total number of cards

Total cards = red cards + black cards = \(3 + 5=8\)

Step2: Calculate number of black cards

Number of black cards \(n(B)=5\)

Step3: Calculate number of red odd - numbered cards

Red odd - numbered cards (red cards are numbered 1 - 3) are 1 and 3. So \(n(R\cap O)=2\) (where \(O\) is the set of odd - numbered cards)

Step4: Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\) (here \(A\) is the event of picking a black card and \(B\) is the event of picking an odd - numbered card)

\(P(\text{black or odd})=\frac{n(B)}{n(T)}+\frac{n(R\cap O)}{n(T)}\) (since \(n(A\cup B)=n(B)+n(R\cap O)\) as there is no overlap between non - black odd cards and black cards in this case)
\(P=\frac{5 + 2}{8}=\frac{7}{8}\)

Answer:

\(\frac{7}{8}\)