Question

a ball is drawn randomly from a jar that contains 3 red balls, 4 white balls, and 5 yellow balls. find the probability of the given event. write your answers as reduced fractions or whole numbers. (a) ( p )(a red ball is drawn) ( = ) (b) ( p )(the ball drawn is not red) ( = ) (c) ( p )(a green ball is drawn) ( = )

Explanation:

Step1: Calculate total number of balls

Total balls = \(3 + 4+5=12\)

Step2: Calculate \(P(\text{A red ball is drawn})\)

Number of red balls = 3. Probability formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P(\text{red})=\frac{3}{12}=\frac{1}{4}\)

Step3: Calculate \(P(\text{The ball drawn is NOT red})\)

Using the formula \(P(\text{not }A)=1 - P(A)\). Since \(P(\text{red})=\frac{1}{4}\), then \(P(\text{not red})=1-\frac{1}{4}=\frac{3}{4}\)

Step4: Calculate \(P(\text{A green ball is drawn})\)

Number of green balls = 0. So \(P(\text{green})=\frac{0}{12}=0\)

Answer:

(a) \(\frac{1}{4}\)
(b) \(\frac{3}{4}\)
(c) \(0\)