Answer:
a) 7/80 = 0.0875
b) 3/16 = 0.1875
c) 1/4 = 0.2500
Step-by-step explanation:
There are a total of 16 balls. 3 are selected. There are ₁₆C₃ possible combinations.
a) If all 3 balls are the same color, they are either all yellow OR all blue OR all red.
The number of ways of choosing 3 yellow balls from 7 is ₇C₃.
The number of ways of choosing 3 blue balls from 5 is ₅C₃.
The number of ways of choosing 3 red balls from 4 is ₄C₃.
The total probability is:
P = (₇C₃ + ₅C₃ + ₄C₃) / ₁₆C₃
P = (35 + 10 + 4) / 560
P = 49 / 560
P = 7 / 80
P = 0.0875
b) The number of ways of choosing 2 yellow balls from 7 is ₇C₂.
The number of ways of choosing 1 blue ball from 5 is ₅C₁.
The probability of both is:
P = ₇C₂ ₅C₁ / ₁₆C₃
P = 21 × 5 / 560
P = 105 / 560
P = 3 / 16
P = 0.1875
c) If all 3 balls are different colors, then there is exactly 1 yellow, 1 blue, and 1 red.
The number of ways of choosing 1 yellow ball from 7 is ₇C₁.
The number of ways of choosing 1 blue ball from 5 is ₅C₁.
The number of ways of choosing 1 red ball from 4 is ₄C₁.
The probability of all events is:
P = ₇C₁ ₅C₁ ₄C₁ / ₁₆C₃
P = 7 × 5 × 4 / 560
P = 140 / 560
P = 1 / 4
P = 0.2500
