Hi JoAnna,
If there are 6 yellow balls and 3 red balls, the chance of drawing a yellow ball is 6/9 (reduced to 2/3) and the chance of drawing a red ball is 3/9 (reduced to 1/3).
1) P(0 yellow balls)
This is the probability of drawing drawing 2 red balls.
(1/3)(1/3) = 1/9
2) P(at least 1 yellow ball)
This the probability of drawing 1 yellow ball or 2 yellow balls.
With regard to 1 yellow ball, it can be drawn 1st or 2nd.
(2/3)(1/3) + (1/3)(2/3) + (2/3)(2/3) = 2/9 + 2/9 + 4/9 = 8/9
3) P(at most 2 yellow balls)
This is the probability of drawing 0 yellow balls, 1 yellow ball, either 1st or 2nd or 2 yellow balls.
(1/3)(1/3) + (1/3)(2/3) + (2/3)(1/3) + (2/3)(2/3) = 1/9 + 2/9 + 2/9 + 4/9 = 9/9 = 1 100%
Seyed Kaveh M.
tutor
Just a quick note. Sometimes in probability, it is easier to use the complement in order to find an answer. Let me show you what I mean.
Take a look at part b, where it says what is the probability of drawing at least one yellow. Here, since you draw only two balls, you can say well, the probability of drawing at least one yellow would be the probability of drawing 1 yellow ball or 2 yellow balls (what Marlene said).
But imagine if you were to pick 100 balls! You don't want to take into account the probability of one yellow, or two yellow, or three yellow,.. or 100 yellow.
Instead you would like to use a shortcut. And here it is!
probability of at least one yellow = 1 - probability (no yellow).
Now from part a, probability no yellow = 1/9
so 1-(1/9) = 8/9
Report
02/10/16
JoAnna N.
You were right. Thanks Syed for pointing it out.
Report
02/11/16
JoAnna N.
02/10/16