Forty toothpicks are used to spell a word—18 blue ones, 10 red ones, 6 yellow ones and 6 green ones. If two toothpicks are selected from the set of forty toothpicks at random in succession and without replacement, what is the probability (as a reduced fraction) of choosing a toothpick that is not red each time?

Question

mathstudent55 · Answer

What is the total number of toothpicks?
How many are not read?

anonymous · Answer

40 toothpicks and 30 are not red

mathstudent55 · Answer

Great.
For the first pick of a toothpick, you want one of the 30 not red ones out of a total of 40 toothpicks. The probability of "not red" for that first pick is 30/40.

mathstudent55 · Answer

A non-red toothpick was already picked.
Now there are a total of 39 toothpicks left.
Out of those, 29 are not red.
The probability of picking a non-red toothpick now is 29/39.

mathstudent55 · Answer

To find the probability of two non-red toothpicks being chosen, you multiply the two probabilities above:

P = 30/40 * 29/39
Multiply the fractions out and reduce.

anonymous · Answer

thnk

mathstudent55 · Answer

wlcm