Question

I NEED HELP - HOMEWORK

Answer 1

Bag 1:  2R, 1B

Bag 2: 1R, 1B, 2Y

Draw 1 from each bag

a) P(same color)

We have 2/3 chance of drawing R from bag 1 and a 1/4 chance of drawing R from bag 2

P(both R) = (2/3)(1/4)  = 1/6

We have a 1/3 chance of drawing B from bag 1 and 1/4 chance of B from bag 2

P(both B) = (1/3)(1/4) = 1/12

P(same color) =1/6 + 1/12 = 3/12 = 1/4

Answer: a) 1/4

b) P(exactly one R)

Same story except we look at the complement in bag 2

We have 2/3 chance of drawing R from bag 1 and a 1/4 chance of drawing R from bag 2, so a 3/4 chance of NOT drawing R.

P(1st red, second not red) = (2/3)(3/4) = 1/2

We have 1/3 chance of drawing B from bag 1, so 1/3 chance of drawing NOT red from bag 1.  We have a 1/4 chance of drawing R from bag 2, so

P(1st blue, second not blue) = (1/3)(1/4) = 1/12

P = 1/2 + 1/12 = 6/12 + 1/12 = 7/12

Answer: 7/12