Question
A bicycle shop rents out bicycles at a park. After lunch, there are 4 black bicycles and
6 silver bicycles remaining to rent. No bicycles are returned and each bicycle is equally likely to be
chosen. Which is the probability that the next two bicycles chosen are silver bicycles?
(
6 silver bicycles remaining to rent. No bicycles are returned and each bicycle is equally likely to be
chosen. Which is the probability that the next two bicycles chosen are silver bicycles?
(
Ask by Rojas Sherman. in the United Arab Emirates
Jan 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability that the next two bicycles chosen are both silver is
.
Solution
To determine the probability that the next two bicycles chosen are both silver, follow these steps:
-
Total Bicycles Available:
- Black Bicycles: 4
- Silver Bicycles: 6
- Total Bicycles: 4 + 6 = 10
-
Probability of Choosing the First Silver Bicycle:
-
Probability of Choosing the Second Silver Bicycle (Without Replacement):
- After choosing one silver bicycle, there are now 5 silver bicycles left and a total of 9 bicycles.
-
Combined Probability:
Final Answer:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
To find the probability that the next two bicycles chosen are silver, we need to calculate the probability of choosing a silver bicycle on the first and second selections. There are a total of 10 bicycles (4 black and 6 silver).
For the first choice, the probability of selecting a silver bicycle is
. After that selection, there are now 5 silver bicycles left out of a total of 9 bicycles. Thus, the probability of choosing a silver bicycle again is
.
Now, multiply these individual probabilities together:
So, the probability that the next two bicycles chosen are silver is
.
Bingo! That’s your winner!