Marble Probability

Question

Given that a box has 3 blue marbles, 2 red marbles, and 4 yellow marbles, use the probability formulas to answer the following questions. Reduce all fractions. Use / as the fraction bar and do not use any spaces. 

Write the probability notion: P(?)

Answers:

1. R ∪ Y
2. Y|R
3. R|Y
4. R  ∩  Y

Answer 1

3B, 2R, 4Y

P(B) = 3/9

P(R) = 2/9

P(Y) = 4/9

P(RUY) = 2/9 + 4/9 = 6/9 = 2/3 chance of red or yellow in one draw

P(Y/R) = 0, zero chance of yellow if it's red in one draw

P(R/Y) = 0 zero chance of red if it's yellow in one draw

P(R intersection Y) = 0 zero chance of both red and yellow in one draw

or if you drew one, then the probability on the next draw is

P(R or Y) P(2R)+P(2Y) + P(R then Y)+ P(Y then R) = (2/9)(1/8)+ (4/9)(3/8) + (2/9)(4/8) + (4/9)(2/8) = 1/36 + 1/6 + 1/9 + 1/9 = (1+6+4+4)/36 = 15/36

P(Y/R) = 4/8 = 1/2

P(R/Y) = 2/8 = 1/4

P(a Red on one draw and yellow on the other) = 2/9 x 1/2 + 4/9 x 2/8 = 1/9+1/9 + 2/9