# Combinations

Algebra

### Combinations

1.If the number p is chosen at random from natural numbers that are not greater than 10, what is the probability 3p + 2 <= 9?
2. If there are 4 red and 2 black balls in the basket, what is the probability that at least one of them is black when two balls are drawn at the same time?
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### Re: Combinations

1.If the number p is chosen at random from natural numbers that are not greater than 10, what is the probability 3p + 2 <= 9?

3p<= 9- 2= 7
p<= 7/3= 2 and 1/3.

Since these are natural numbers that is the same as saying that p= 1 or p= 2. Assuming that all numbers from 1 to 10 are equally likely to be chosen, the probability is 1/10+ 1/10= 2/10= 1/5.

2. If there are 4 red and 2 black balls in the basket, what is the probability that at least one of them is black when two balls are drawn at the same time?

The only way there could not be "at least one black ball" is if both balls are red. There are 4 red and 2 black balls so the probability ball A is red is 4/(4+ 2)= 4/6= 2/3. Given that, there are 5 balls left, 3 red and 2 black, so the probability ball B is also red is 3/(3+ 2)= 3/5. The probability the two balls are both red is (2/3)(3/5)= 2/5. The probability "at least one ball is black" is 1- 2/5= 3/5.

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