Question

a bag contains only yellow marbles and red marbles. the probability of selecting a yellow marble from the bag at random is \\( \frac{1}{13} \\). what is the probability of selecting a red marble from the bag at random?

Explanation:

Step1: Use probability formula

The sum of probabilities of all possible outcomes is \(1\). Let \(P(Y)\) be the probability of selecting a yellow marble and \(P(R)\) be the probability of selecting a red marble. We know \(P(Y)=\frac{1}{3}\), and \(P(Y)+P(R) = 1\).

Step2: Solve for \(P(R)\)

Substitute \(P(Y)\) into the formula: \(P(R)=1 - P(Y)\). So \(P(R)=1-\frac{1}{3}=\frac{3 - 1}{3}=\frac{2}{3}\approx0.6667\)

Answer:

\(\frac{2}{3}\) (or \(0.667\) if decimal is preferred)