Part 4 or 6 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 slof 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 wheet is spun 1000 times, it is expected that about 21 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 . (c) Determine the probability that the metal ball lands in an odd slot. Interpret this probability. The probabillty that the metal ball lands in an odd slot is $$ \square $$ . (Round to four decimal places as needed.)

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**(a)**  
The wheel contains 48 slots labeled with the symbols  
$$
\{00,\, 0,\, 1,\, 2,\, \ldots,\, 46\}.
$$  
Thus, the sample space is  
$$
\{00,\, 0,\, 1,\, 2,\, \ldots,\, 46\}.
$$  
**Answer: Choice A.**

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**(b)**  
Since there is exactly one slot labeled $$4$$ in the set of 48 slots, the probability that the metal ball falls into slot $$4$$ is  
$$
P(4) = \frac{1}{48} \approx 0.0208.
$$

To interpret this probability: If the wheel is spun 1000 times, then the expected number of times the ball lands on slot $$4$$ is  
$$
1000 \times \frac{1}{48} \approx 20.8333,
$$  
which rounds to about $$21$$ times.

**Answer: The probability is $$ \frac{1}{48}$$ (approximately $$0.0208$$), and if the wheel is spun 1000 times, it is expected that about $$21$$ of those spins result in the ball landing in slot $$4$$.**

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**(c)**  
To find the probability of landing in an odd slot, first identify the odd-numbered slots within the set. Excluding the slots labeled $$00$$ and $$0$$ (which represent $$0$$, an even number), the remaining slots are  
$$
\{1,\, 2,\, 3,\, \ldots,\, 46\}.
$$  
Within these, the odd slots are  
$$
\{1,\, 3,\, 5,\, \ldots,\, 45\}.
$$

To count the number of odd numbers between $$1$$ and $$46$$:
- The smallest odd number is $$1$$.
- The largest odd number less than or equal to $$46$$ is $$45$$.

The count is given by  
$$
\text{Number of odds} = \frac{45 - 1}{2} + 1 = \frac{44}{2} + 1 = 22 + 1 = 23.
$$

Thus, there are $$23$$ odd-numbered slots out of $$48$$ slots in total. The probability that the metal ball lands in an odd slot is  
$$
P(\text{odd}) = \frac{23}{48} \approx 0.4792.
$$

**Answer:** The probability is $$\frac{23}{48}$$ (approximately $$0.4792$$).  
Interpreting this: If the wheel is spun 1000 times, one would expect that about  
$$
1000 \times 0.4792 \approx 479
$$
spins result in the ball landing in an odd slot.
**(a)** The sample space is all the numbered slots on the wheel: $$ \{00,\, 0,\, 1,\, 2,\, \ldots,\, 46\}. $$ **Answer: Choice A.** **(b)** The probability that the ball lands on slot $$4$$ is $$ \frac{1}{48} \approx 0.0208. $$ If the wheel is spun 1000 times, it is expected that about $$21$$ times the ball will land on slot $$4$$. **(c)** There are $$23$$ odd-numbered slots out of $$48$$. The probability of landing on an odd slot is $$ \frac{23}{48} \approx 0.4792. $$ If the wheel is spun 1000 times, it is expected that about $$479$$ times the ball will land on an odd slot.

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