The total number of balls in the bag is:
6 (white balls) + 4 (black balls) = 10 balls
The total number of ways to choose 2 balls out of 10 is given by the combination formula \(\binom{n}{r}\):
\(\binom{10}{2} = \frac{10 \times 9}{2 \times 1} = 45\)
The number of ways to choose 2 white balls out of 6 is:
\(\binom{6}{2} = \frac{6 \times 5}{2 \times 1} = 15\)
The probability of drawing 2 white balls is the ratio of the number of favorable outcomes (drawing 2 white balls) to the total number of possible outcomes (drawing 2 balls):
P(both white) = \(\frac{\binom{6}{2}}{\binom{10}{2}} = \frac{15}{45} = \frac{1}{3}\)
Comparing \(\frac{1}{3}\) with \(\frac{z}{3y}\), we see that z = 1 and y = 1.
z + y
= 1 + 1
= 2
Thus, the value of z + y = 2.
