Answer:
(i) 1/21
(ii) 1/10
(iii) Take a look at the explanation: Try this one yourself. I have given you some hints.
Step-by-step explanation:
(i) Two red balls:
To do this, we need to find the total amount of possible choices first. To do this, we multiply 15 by 14. This is our denominator:
15(14) = 210
Now, we need to find the total combinations of red balls. We solve 5 choose 2 for this one.
5 choose 2 = 5(4)/2! = 10
Our numerator is 10. Therefore, our probability is 10/210 = 1/21.
(ii) Two blue balls or two black balls:
To do this, we need to add the probabilities of getting a blue ball with a black ball. (Since there is an "or" sitting there. If there is an "and", we multiply)
So, let's calculate the probability of getting a blue ball first:
Blue:
We use the same denominator as before: 210.
Our numerator is now 6 choose 2, which is:
6 choose 2 = 6(5)/2! = 15.
Now, our fraction is 15/210, BUT, dont simplify, as we will need to add.
Black:
Same steps: denominator is 210, but the numerator is 4 choose 2.
Solving 4 choose 2:
4 choose 2 = 4(3)/2! = 6.
Our numberator is 6.
But, we cant forget to add them!
(15 + 6)/210 is 21/210, which is 1/10.
(iii) I'll let you try this one by yourself. Here is a hint:
Solve for the probability of chooseing a black ball and a red ball. Then, multiply.
Enjoy the process, and I hoped this helped you! (If you have any questions, feel free to ask)
