Question

Help! 5 balls are selected at random, assume that the bucket contains 6 orange balls and 7 yellow balls.

What is the probability that, of the 5 balls selected at random, at least one is orange and at least one is yellow?

Answer 1

Would it be something like:
6C1 * 7C1 *??
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13C5

Answer 2

lol. balls.

Answer 3

Are the balls replaced after each pick?

Answer 4

I don't think so

Answer 5

Can also consider the chance of not getting one of a particular color and using the complement.

Answer 6

I'm not sure what to do here

Answer 7

It is hard to tell from the wording whether there is replacement or not. My instinct says that it is without replacement. The probability of getting at least one of something is the same as the probability of not getting none. There are two possibilities for that: Not getting any orange, and not getting any yellow.

if you are working under the assumption of no replacement remember to change both numerator and denominator of your probabilities.

Answer 8

Could you show me how to do this type of problem? I have others like it, so once I know how to do this I can do the others

Answer 9

@mathmate please help

Answer 10

They are picked simultaneously

Answer 11

wouldnt it be 2/13?

Answer 12

why?

Answer 13

ugh its hard to explain but i think it is. ill think more about it thou

Answer 14

I don't

Answer 15

How did you do it?

Answer 16

It's probability theory

Answer 17

Assuming selection of 5 balls at random \( \textit without \) replacement.
We need the probability of drawing at least one of each colour.

Any ball drawn is either orange or yellow, which eliminates the case of neither orange nor yellow.
So the only "unsuccessful" cases are only orange or only yellow.
Therefore
\( P(O\cap Y) = 1-( P(all\ orange) + P(all\ yellow)) \)

Answer 18

Thank you!!!!