Thread: probability

"Assume that the box contains 7 balls: 4 red, 2 green, and 1 yellow. Balls are drawn in succession without replacement, and their colors are noted until both a red and a green ball have been drawn."

How many outcomes are there in the sample space?"


the answer is 25, but i only know how to arrive at this answer by sketching a convoluted diagram or by racking my brain to figure out all the sets (RG, RRG, RRRG etc) and then counting the outcomes.

is there a faster way to figure out the number of outcomes using algebra or some other method? i don't think i'll have enough time on the test to draw a diagram.


thanks

Originally Posted by sdsdsd

"Assume that the box contains 7 balls: 4 red, 2 green, and 1 yellow. Balls are drawn in succession without replacement, and their colors are noted until both a red and a green ball have been drawn."

How many outcomes are there in the sample space?"


the answer is 25, but i only know how to arrive at this answer by sketching a convoluted diagram or by racking my brain to figure out all the sets (RG, RRG, RRRG etc) and then counting the outcomes.

is there a faster way to figure out the number of outcomes using algebra or some other method? i don't think i'll have enough time on the test to draw a diagram.


thanks

I don't see too many short cuts here.

Hello, sdsdsd!

I agree with Mr. F . . . I see no "formula" approach.
I think Brute Force listing is the only way . . .


Two draws

. . . 2 ways.


Three draws

. . . 6 ways


Four draws

. . . 7 ways


Five draws

. . . 5 ways


Six draws

. . . 5 ways


Total: 25 ways