Question

a jar contains 4 red marbles numbered 1 to 4, 8 blue marbles numbered 1 to 8, and 10 white marbles numbered 1 to 10. a marble is drawn at random from the jar. find the probability of the given event. write your answers as integers or reduced fractions. (a) the marble is red. (b) the marble is not red. (c) the marble has the number 1 written on it. (d) the marble is blue with the number 2 written on it. (e) the marble has the number 16 written on it.

Explanation:

Step1: Calculate total marbles

Total marbles = 4 (red) + 8 (blue) + 10 (white) = 22

Step2: Calculate probability for (a)

Probability (red) = $\frac{\text{Number of red marbles}}{\text{Total marbles}}=\frac{4}{22}=\frac{2}{11}$

Step3: Calculate probability for (b)

Probability (not red) = 1 - Probability (red) = $1-\frac{2}{11}=\frac{9}{11}$

Step4: Calculate probability for (c)

There is 1 red - numbered 1, 1 blue - numbered 1, 1 white - numbered 1. So 3 marbles with 1 written on them. Probability = $\frac{3}{22}$

Step5: Calculate probability for (d)

There is 1 blue marble numbered 2. Probability = $\frac{1}{22}$

Step6: Calculate probability for (e)

No marble has 16 written on it. Probability = 0

Answer:

(a) $\frac{2}{11}$
(b) $\frac{9}{11}$
(c) $\frac{3}{22}$
(d) $\frac{1}{22}$
(e) 0