Question 1120786
<br>
When given the ratio of P:Q and the ratio of Q:R, you can get a ratio of all three by making the value of Q in both ratios the same:<br>
P:Q = 2:1 and Q:R = 4:5  -->  P:Q = 8:4 and Q:R = 4:5<br>
Then P:Q:R = 8:4:5<br>
Now, given that ratio,
let P = 8x
let Q = 4x
let R = 5x<br>
Then after all the balls are mixed together, 8/17 of them are red (P), 4/17 are blue (Q), and 5/17 are white (R).<br>
(a) The probability of picking a red ball is 8/17.<br>
(b)(i) To pick a white and a blue with replacement, you can pick either a white first and then a blue, or a blue first and then  white.
P(white, blue) = (5/17)(4/17) = 20/289
P(blue, white) = (4/17)(5,17) = 20/289
P(one blue and one white) = 40/289<br>
(b)(ii) The probability of drawing a blue and then a red is (4/17)(8/17) = 32/289.