Question

you pick a card at random.
what is p(not factor of 72)?
write your answer as a fraction or whole number.

Explanation:

Step1: Find total number of cards

There are \(5\) cards in total. So, total number of outcomes \(n = 5\).

Step2: Find factors of \(72\) among the cards

Factors of \(72\) are numbers that divide \(72\) evenly.

• \(72\div5 = 14.4\) (not a factor)
• \(72\div6=12\) (a factor)
• \(72\div7\approx10.29\) (not a factor)
• \(72\div8 = 9\) (a factor)
• \(72\div9=8\) (a factor)

Numbers that are factors of \(72\) among the cards: \(6\), \(8\), \(9\). So, number of favorable outcomes (for factor of \(72\)) \(m_1=3\).

Step3: Find number of non - factors of \(72\)

Number of non - factors of \(72\) (favorable outcomes for not factor of \(72\)) \(m_2=n - m_1\).
\(m_2=5 - 3=2\).

Step4: Calculate the probability

Probability formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
\(P(\text{not factor of }72)=\frac{2}{5}\)

Answer:

\(\frac{2}{5}\)