Calculating Probability of Winning Candy for 10 Students

Click For Summary
SUMMARY

The probability of winning candy for the day among 10 students drawing from a bag containing 9 white marbles and 1 black marble is not equal for all students. The third student in line has a specific probability of winning calculated as 1/8 * 9/10 * 8/9, which accounts for the scenarios where the first two students do not draw the black marble. This calculation confirms that the third student does have a chance to win, and the overall probability distribution is influenced by the order of drawing.

PREREQUISITES
  • Understanding of basic probability concepts
  • Familiarity with combinatorial calculations
  • Knowledge of sequential events in probability
  • Ability to interpret mathematical expressions
NEXT STEPS
  • Study the fundamentals of probability theory
  • Learn about conditional probability and its applications
  • Explore combinatorial probability techniques
  • Practice calculating probabilities in sequential drawing scenarios
USEFUL FOR

Students, educators, and anyone interested in probability theory, particularly in understanding sequential events and their impact on outcomes.

Shanelani2006
Messages
1
Reaction score
0
There are 10 marbles in a bag, 9 white and 1 black. Each day a teacher goes around the room of 10 students and allows each student to pick one marble. The one who draws the black marble gets candy for the day. The students never change their seats and she always distribute the marbles along the same path (the first person is always the first person to draw and the last person is always the last to draw). Does each student have an equal chance to win candy for the day? How would the probability be calculated for third person in line?
I thought every student has an equal chance of 10% an the probability for the third person would be 1/8*9/10*8/9 (the prob. that 3rd person draws it times the prob. that the first person did not draw it times the prob. that the 2nd person didnt draw it) But i don't know if i am making a wrong asumption that the third person even has a chance. please help
 
Physics news on Phys.org
Your analysis sounds fine to me.
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 17 ·
Replies
17
Views
4K
  • · Replies 2 ·
Replies
2
Views
6K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
6
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
7
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
Replies
3
Views
2K