Probability question

Question

A bag contains three red counters, four green counters, two yellow counters and one white counter. Two counters are drawn from the bag one after the other, without being replaced.

Calculate:

 P(white or yellow, in either order but not both)

P(white or red, in either order but not both).

Answer 1

Total number of counters=3+4+2+1=10. Probability of first counter being white is 0.1; and yellow is 0.2.

Probability of white then yellow = 0.1×2/9=0.2/9; yellow then white = 0.2×1/9=0.2/9. These are mutually exclusive events so the combined probability = 0.4/9=4/90=2/45.

Probability of white then red = 0.1×3/9=0.1/3; red then white = 0.3×1/9=0.3/9=0.1/3. These are mutually exclusive events so the combined probability = 0.2/3=2/30=1/15.