h 120 Intro Prob and Stats HW Score: 48\%, 24 of 50 points Save Question 24, 5.1.27 Points: 0 of 1 $$ 10(5.1,5.2) $$ Part of 5 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 $$ \{00,0,1,2, \ldots, 46\} $$. B. The sample space is $$ \{1,2, \ldots, 46\} $$. C. The sample space is $$ \{00\} $$. D. The sample space is $$ \{00,0\} $$. (b) Determine the probability that the metal ball falls into the slot marked 4. Interpret this probability. The probability that the metal ball falls into the slot marked 4 is $$ \square $$ 0.0208 (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Type a whole number.) A. If the wheel is spun 1000 times, it is expected that about $$ \square $$ of those times result in the ball landing in slot 4 . B. If the wheel is spun 1000 times, it is expected that exactly $$ \square $$ of those times result in the ball not landing in slot 4 .

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**(a)**  
There are 48 numbered slots on the wheel, including two specially labeled slots: $$00$$ and $$0$$, followed by the numbers $$1, 2, \ldots, 46$$.   
Thus, the sample space is  
$$
\{00,\,0,\,1,\,2,\,\ldots,\,46\}.
$$  
Answer: **A.**

**(b)**  
The probability of the ball landing in a particular slot, say slot $$4$$, is determined by  
$$
P(4) = \frac{1}{\text{total number of slots}} = \frac{1}{48} \approx 0.0208.
$$

To interpret this probability, consider repeated spins. If the wheel is spun 1000 times, the expected number of times $$E$$ that the ball lands in slot $$4$$ is  
$$
E = 1000 \times \frac{1}{48} \approx 20.8333.
$$
Rounded to a whole number, one would expect about $$21$$ outcomes.

Answer interpretation:  
A. If the wheel is spun 1000 times, it is expected that about **21** of those times result in the ball landing in slot 4.
**(a)** The sample space is all 48 numbered slots: $$ \{00,\,0,\,1,\,2,\,\ldots,\,46\}. $$ Answer: **A.** **(b)** The probability of landing on slot 4 is $$ P(4) = \frac{1}{48} \approx 0.0208. $$ Interpretation: A. If the wheel is spun 1000 times, it is expected that about **21** of those times result in the ball landing in slot 4.

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