Probability of Choosing 7 out of 32

addaman

New member
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Dec 10, 2016
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What are the odds/probability of choosing
7 Red Marbles from a jar mixed with 25 White marbles
IF you are blindfolded and the marbles may not be differentiated by
any other mean(Similar size, texture, etc..) ?

What are the odds of doing it upon your first attempt?
 
Okay, so if I understand you correctly, the problem statement asks you to find the odds of drawing 7 marbles of out of the 32 and having all of them be red (and thus none white). Is that correct? If not, please provide any necessary corrections, ideally by providing the full and exact text of the problem statement.

Assuming the above interpretation is correct, here's some questions to maybe guide you in the right direction. What is the odds of your first marble being red? What is the odds of your second marble being red? The third marble? Are you seeing a pattern? Repeat for all seven marbles. Now, with that data in hand, what are the odds of all seven of these independent events happening? Another thing you might consider is: Does the problem say if you replace the marbles after drawing or not? Would that change the odds? If so, how?
 
Assuming you mean that there are exactly 7 red marbles and 25 white marbles then:

There are initially 32 marbles, 7 of them red. The probability the first marble drawn is red is 7/32.

There are then 31 marbles left, 6 of them red. The probability the second marble drawn is red is 6/31. The probability the first two marbles drawn are both red is (7/32)(6/31).

There are then 30 marbles left, 5 of them red. The probability the third marble drawn is red is 5/30. The probability the first two marbles drawn are both red is (7/32)(6/31)(5/30).

There are then 29 marbles left, 4 of them red. The probability the fourth marble drawn is red is 4/29. The probability the first two marbles drawn are both red is (7/32)(6/31)(5/30)(4/29).

Get the point? Continue that until you have all 7 red marbles.
 
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