Playing Good Golf

white golf bags

A golf bag contains 6 white balls and 8 yellow balls.
Therefore, there are (6+8) balls overall = 14 balls.

To draw one white ball is a 6/14 chance.
However, the ball is not replaced in the bag, so the total count goes to 5 white balls, 8 yellow, and 13 total.
To draw another white ball is a 5/13 chance therefore.
The total count now goes to 4 white balls, 8 yellow, and 12 total.
To draw another white ball is a 4/12 chance therefore.

Where you want a probability of an event, AND another, you need to times them together.

a) (6/14) * (5/13) * (4/12) = (5/91)

——-

To draw one yellow ball (assuming all balls are now back in the bag) is a 8/14 chance.
The total count now goes to 6 white balls, 7 yellow, and 13 total.
To now draw a white ball is a 6/13 chance.
(8/14) * (6/13) = (24/91)

However – you aren’t done yet!
To get the same result, you can also draw the balls the other way around – i.e. if you draw a white ball and then a yellow.

To draw one white ball (assuming all balls are now back in the bag) is a 6/14 chance.
The total count now goes to 5 white balls, 8 yellow, and 13 total.
To now draw a yellow ball is a 8/13 chance.
(6/14) * (8/13) = (24/91).

Adding the two probabilities together because they are both what you want. (An OR function)

b) (24/91) + (24/91) = (48/91)

Hope this helps!

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