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Question 8, 5.1.27
HW Score: $28.79 \%, 6.33$ of 22 points
Part 3 of 5
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In a certain game of chance, a wheel consists of 50 slots numbered $00,0,1,2, \ldots, 48$. 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 $\{1,2, \ldots, 4\}$
B. The sample space is $\{00,0\}$
C. The sample space is $\{00\}$
D. The sample space is $\{00,0,1,2,48\}$
(b) Determine the probability that the metal ball falls into the slot marked 7 . Interpret this probability
The probability that the metal ball falls into the slot marked 7 is 0.02
(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 7
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 7 .
Answer
The probability that the ball falls into the slot marked 7 is given as 0.02. This means that if the game is played many times, we expect the ball to fall into the slot marked 7 about 2% of the time. To interpret this probability, we can multiply the probability by the number of times the game is played. For example, if the game is played 1000 times, we expect the ball to fall into the slot marked 7 about \(0.02 * 1000 = 20\) times. So, if the wheel is spun 1000 times, it is expected that about \(\boxed{20}\) of those times result in the ball landing in slot 7.
Step 1 ：The sample space is the set of all possible outcomes. In this case, it's all the numbers that the ball can fall into, which are 00, 0, 1, 2, ..., 48. So, the sample space is \(\boxed{\{00,0,1,2, \ldots, 48\}}\).
Step 2 ：The probability that the ball falls into the slot marked 7 is given as 0.02. This means that if the game is played many times, we expect the ball to fall into the slot marked 7 about 2% of the time. To interpret this probability, we can multiply the probability by the number of times the game is played. For example, if the game is played 1000 times, we expect the ball to fall into the slot marked 7 about \(0.02 * 1000 = 20\) times. So, if the wheel is spun 1000 times, it is expected that about \(\boxed{20}\) of those times result in the ball landing in slot 7.
