Question

How can I find the probability?

A box contains 4 yellow and 5 black balls. A ball is drawn from the box and is not
replaced, then a second ball is drawn. Find the probability of:
yellow then black being drawn,
black then yellow being drawn,
both balls being yellow
both balls being black
drawing yellow and black in any order

Answer 1

P[yellow then black]=`4/9 xx 5/8=20/72=5/18`

P[black then yellow]=`5/9 xx 4/8=20/72=5/18`

P[yellow then yellow]=`4/9 xx 3/8=12/72=1/6`

P[black then black]=`5/9 xx 4/8=20/72=5/18`

Probability of yellow and black in either order is

= `5/18+5/18=10/18=5/9`

Explanation:

P[yellow]=`4/9` as there are 4 yellows and 9 balls in total
P[black]=`5/8` as there are 5 blacks but only 8 balls as the yellow was not put back.
P[yellow then black]=`4/9 xx 5/8=20/72=5/18`

P[black then yellow]=`5/9 xx 4/8=20/72=5/18`

P[yellow then yellow]=`4/9 xx 3/8=12/72=1/6`

P[black then black]=`5/9 xx 4/8=20/72=5/18`

Probability of yellow and black in either order is

P[yellow then black] + P[black then yellow]

= `5/18+5/18=10/18=5/9`