a bag contains two black balls, three green balls and four
red balls.
That's a total of 2 blacks + 3 greens + 4 reds = 9 balls
A ball is picked from the bag at random. What
is the probability that it is;
1. black
That's 2 black balls out of 9 balls, so the probability is 2/9.
That doesn't reduce so we leave it 2/9.
2. green
That's 3 green balls out of 9 balls, so the probability is 3/9.
That reduces to 1/3
3. red
That's 4 red balls out of 9 balls, so the probability is 4/9.
That doesn't reduce so we leave it 4/9.
4. yellow
There are no yellow balls in the bag.
That's 0 yellow balls out of 9 balls, so the probability is 0/9,
which is just 0. When something is impossible, its probability
is 0.
5. not black
There are 3+4 or 7 balls that are not black, because 3 are green
and 4 are red.
That's 7 non-black balls out of 9 balls, so the probability is 7/9.
That doesn't reduce so we leave it 7/9.
6. either black or red?
There are 2+4 or 6 balls that are either black or red, because 2
are black and 4 are red.
That's 6 black or red balls out of 9 balls, so the probability
is 6/9. That reduces to 2/3.
Edwin