Three red balls, five green balls, and a number of blue balls are put together in a sack. One ball is picked at random from the sack. If the probability of picking a red ball is \(\frac{1}{6}\) find;
(a) Let the number of blue balls be x.
The probability of picking a red ball is 1/6, which means there is only one red ball in the sack.
Therefore, the total number of balls in the sack is:
1 (red ball) + 5 (green balls) + x (blue balls) = 6 + x
The probability of picking a red ball is the number of red balls in the sack divided by the total number of balls in the sack. So we can write:
1/(6 + x) = 1/6
Solving for x, we get:
6 + x = 6
x = 0
Therefore, there are 0 blue balls in the sack.
(b) The probability of picking a green ball is the number of green balls in the sack divided by the total number of balls in the sack.
Since we know there are 5 green balls and 1 red ball in the sack (and 0 blue balls, as we found in part (a)), the total number of balls in the sack is:
1 (red ball) + 5 (green balls) + 0 (blue balls) = 6
So the probability of picking a green ball is:
5/6
Therefore, the probability of picking a green ball is 5/6.