Question
A roulette wheel has 34 slots around the rim; 32 slots are numbered from 1 to 32 . Half of these 32 slots are red, and the
other half are black. The remaining 2 slots are numbered 0 and 00 and are green. As the roulette wheel is spun in
one direction, a small ivory ball is rolled along the rim in the opposite direction. The ball has an equality likely chance of
falling into any one of the 34 slots. Find the probabilities of the events listed in parts (a) through (d) below.
a. Ball lands in a red slot
The probability of the event that the ball lands in a red slot is
(Type an integer or a simplified fraction.)
b. Ball lands on 0 or 32
The probability of the event that the ball lands on 0 or 32 is
(Type an integer or a simplified fraction.)
c. Ball does not land on a number from 6 through 28
The probability of the event that the ball does not land on a number from 6 through 28 is
(Type an integer or a simplified fraction.)
d. Ball lands on an odd number or on a green slot
The probability of the event that the ball lands on an odd number or on a green slot is
(Type an integer or a simplified fraction.)
other half are black. The remaining 2 slots are numbered 0 and 00 and are green. As the roulette wheel is spun in
one direction, a small ivory ball is rolled along the rim in the opposite direction. The ball has an equality likely chance of
falling into any one of the 34 slots. Find the probabilities of the events listed in parts (a) through (d) below.
a. Ball lands in a red slot
The probability of the event that the ball lands in a red slot is
(Type an integer or a simplified fraction.)
b. Ball lands on 0 or 32
The probability of the event that the ball lands on 0 or 32 is
(Type an integer or a simplified fraction.)
c. Ball does not land on a number from 6 through 28
The probability of the event that the ball does not land on a number from 6 through 28 is
(Type an integer or a simplified fraction.)
d. Ball lands on an odd number or on a green slot
The probability of the event that the ball lands on an odd number or on a green slot is
(Type an integer or a simplified fraction.)
Ask by Page Johnston. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability that the ball lands on an odd number or on a green slot is
Solution
To solve part (d), we need to determine the probability that the ball lands on an odd number or on a green slot.
Details of the Roulette Wheel:
- Total Slots: 34
- Numbered Slots: 32 (numbered from 1 to 32)
- Red Slots: 16
- Black Slots: 16
- Green Slots: 2 (numbered 0 and 00)
- Numbered Slots: 32 (numbered from 1 to 32)
Calculating the Probability:
-
Odd Numbers:
- The numbers range from 1 to 32.
- Number of Odd Numbers: 16 (since half of the numbers from 1 to 32 are odd).
-
Green Slots:
- There are 2 green slots: 0 and 00.
-
Total Favorable Outcomes:
- Odd Numbers: 16
- Green Slots: 2
- Total:
-
Total Possible Outcomes:
- 34 slots in total.
-
Probability:
- Simplifying the fraction:
Final Answer:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Explain 
Simplify this solution Mind Expander
To find the probability of the events listed, let’s break down the information we know:
a. For the red slots, there are 16 red slots (half of 32). Therefore, the probability that the ball lands in a red slot is
b. For the event that the ball lands on 0 or 32, there are 2 favorable outcomes (0 and 32) out of 34 total slots. Thus, the probability is
c. The numbers from 6 through 28 are
d. To find the probability of landing on an odd number or a green slot:
- The odd numbers from 1 to 32:
, which gives us 16 odd numbers. - We also have the two green slots:
and .
Now, let’s count:
- Odd numbers = 16
- Green slots = 2
- There is no overlap between these two sets, so we can simply add them.
Total favorable outcomes = 16 (odd numbers) + 2 (green) = 18.
Thus, the probability of landing on an odd number or green is:
Summarizing:
a. Ball lands in a red slot:
b. Ball lands on 0 or 32:
c. Ball does not land on a number from 6 through 28:
d. Ball lands on an odd number or on a green slot:
a. Ball lands in a red slot:
b. Ball lands on 0 or 32:
c. Ball does not land on a number from 6 through 28:
d. Ball lands on an odd number or on a green slot:
