Ik $$ 10(5.1,5.2) $$ In a certain game of chance, a wheel consists of 48 slots numbered $$ 00,0,1,2, \ldots, 46 $$. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. Complete parts (a) through (c) below. (a) Determine the sample space. Choose the correct answer below. A. The sample space is $$ \{00,0,1,2, \ldots, 46\} $$. C. The sample space is $$ \{1,2, \ldots, 46\} $$. D. The sample space is $$ \{00\} $$. (b) Determine the probability that the metal ball falls into the slot marked $$ 400,5.1 .27 $$. Interpret this probability. The probability that the metal ball falls into the slot marked 4 is (Round to four decimal places as needed.)

Question

UpStudy AI · Accepted Answer

Let's solve the problem step by step.

### Part (a): Determine the Sample Space

The sample space is the set of all possible outcomes of an experiment. In this case, the experiment involves spinning a wheel with slots numbered from $$00$$ to $$46$$.

The slots are:
- $$00$$
- $$0$$
- $$1$$
- $$2$$
- ...
- $$46$$

Thus, the complete sample space is:
$$
\{00, 0, 1, 2, \ldots, 46\}
$$

So, the correct answer is:
**A. The sample space is $$ \{00,0,1,2, \ldots, 46\} $$.**

### Part (b): Determine the Probability

To find the probability that the metal ball falls into a specific slot, we use the formula for probability:
$$
P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
$$

In this case:
- The total number of outcomes (the number of slots) is $$48$$.
- The number of favorable outcomes for the ball falling into a specific slot (e.g., slot marked $$4$$) is $$1$$.

Thus, the probability $$P(4)$$ is:
$$
P(4) = \frac{1}{48}
$$

Now, let's calculate this probability and round it to four decimal places:
$$
P(4) = \frac{1}{48} \approx 0.0208333
$$

Rounding to four decimal places:
$$
P(4) \approx 0.0208
$$

### Interpretation of the Probability

The probability that the metal ball falls into the slot marked $$4$$ is approximately $$0.0208$$. This means that there is about a $$2.08\%$$ chance that the ball will land in the slot marked $$4$$ when the wheel is spun.

### Summary of Answers
- (a) The sample space is $$ \{00,0,1,2, \ldots, 46\} $$.
- (b) The probability that the metal ball falls into the slot marked $$4$$ is approximately $$0.0208$$.
- **Part (a):** The sample space is all numbers from $$00$$ to $$46$$. - **Part (b):** The probability of the ball landing on $$4$$ is approximately $$0.0208$$.

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Probability Questions