r + w = 10 --> w = 10 – r
This is a very good approach you use.
out of statement (2),
(r/10) × (w/9) = (7/15)
Here is a mistake you've made. The left side of the equality defines the probability of the following event:
"We choose two marbles, one at a time. The first marble is red. The second marble is white."
But the question and statement (2) deal with the event "two marbles are chosen at the same time. One of them is red, another one is white."
Try to feel the difference. ... Now, if to convert "two marbles are chosen at the same time" into "we choose two marbles, one at a time", then "one of them is red, another one is white" consists of two possibilities
- "the first one is red, the second one is white"
- "the first one is white, the second one is red".
Therefore your equation should be the following:
/9) + (w
/9) = (7/15)
Simplify it first, then plug in w
= 10 – r
and you'll get two solutions (w
= 7, r
= 3 and w
= 3, r
, you can deal with selected pairs (imagine we numbered marbles and select two at once). For statement (2) there will be w
such pairs (one white and one red). The total number of possible pairs will be 2-combinations of 10 elements (10 C 2 = 10!/(8! × 2!) = 45).
The equation will be the same wr
/45 = 7/15.