eight balls numbered 1 to 8 are placed in a bag. some of the balls are grey and some are white. the balls…
eight balls numbered 1 to 8 are placed in a bag. some of the balls are grey and some are white. the balls numbered 3, 4, and 6 are grey. the balls numbered 1, 2, 5, 7, and 8 are white. a ball will be selected from the bag at random. the 8 possible outcomes are listed below. note that each outcome has the same probability. complete parts (a) through (c). write the probabilities as fractions. (a) check the outcomes for each event below. then, enter the probability of the event. event a: the selected ball has an odd number on it event b: the selected ball is grey
Answer
Explanation:
Step1: Identify odd - numbered balls
Odd - numbered balls are 1, 3, 5, 7. There are 4 odd - numbered balls out of 8 total balls.
Step2: Calculate probability of Event A
The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P(A)=\frac{4}{8}=\frac{1}{2}$.
Step3: Identify grey balls
Grey balls are 3, 4, 6. There are 3 grey balls out of 8 total balls.
Step4: Calculate probability of Event B
Using the probability formula $P(B)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$, we get $P(B)=\frac{3}{8}$.
Answer:
Event A:
| Outcomes | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Probability |
|---|---|---|---|---|---|---|---|---|---|
| $\boxed{\surd}$ | $\boxed{\surd}$ | $\boxed{\surd}$ | $\boxed{\surd}$ | $\frac{1}{2}$ | |||||
| Event B: | |||||||||
| Outcomes | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Probability |
| ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- |
| $\boxed{\surd}$ | $\boxed{\surd}$ | $\boxed{\surd}$ | $\frac{3}{8}$ |