Stones of Probability

Probability Level 3

I have a bag, which contains $3$ red stones and $4$ blue stones.

If I randomly take out the stones one by one and then lay them out in order of appearance, what is the probability that there are three (or more) stones of matching color in a row?

\frac 25

\frac7{35}

\frac{17}{35}

\frac{19}{35}

Impossible to solve

1 solution

Geoff Pilling
Oct 29, 2018

There is one way of having 3 reds in a row without 3 blues being in a row (First one shown above), since we are counting the blues below and don't want to double count.

4 ways of having 4 blues together.

12 ways of having 3 (but not 4) blues together

3 ways the first three can be blue: BBBRXXX
2 ways the 2nd through 4th can be blue: RBBBRXX
2 ways the middle three can be blue: XRBBBRX
2 ways the 4th through 6th can be blue: XXRBBBR
3 ways the last three can be blue: XXXRBBB

$1 + 4 + 12 = 17$

And there are $\binom{7}{3} = 35$ ways to pick them.

$P = \dfrac{17}{35}$

Stones of Probability

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