Question

a toy store sells individual marbles in a variety of colors and sizes.
what is the probability that a randomly selected marble is purple or is not small?
simplify any fractions.

Explanation:

Step1: Calculate the total number of marbles

Add up all the values in the table: \(5 + 8+2 + 4+6 + 9=\sum_{i = 1}^{6}x_{i}=34\)

Step2: Calculate the number of purple marbles

\(2 + 9=11\)

Step3: Calculate the number of non - small (big) marbles

\(5+8 + 2=15\)

Step4: Calculate the number of marbles that are purple and big

\(2\)

Step5: Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

Let \(A\) be the event that the marble is purple and \(B\) be the event that the marble is not small.
\(P(A)=\frac{11}{34}\), \(P(B)=\frac{15}{34}\), \(P(A\cap B)=\frac{2}{34}\)
\(P(A\cup B)=\frac{11 + 15- 2}{34}=\frac{24}{34}=\frac{12}{17}\)

Answer:

\(\frac{12}{17}\)