A running total

Probability Level 3

A spinner is split into 3 equal regions, and numbers 1, 2 and 3 are assigned to regions one, two and three respectively. Assume that it is equally probable that the pointer will land on any one of the three regions. If the pointer lands on the borderline, spin again. You keep spinning it and keeping a running total. You start with a total of zero and keep adding the number shown on the region after every spin. Find the probability to get a total of 3.

14 27 \frac{14}{27} 5 9 \frac{5}{9} 11 21 \frac{11}{21} 16 27 \frac{16}{27}

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Jeremy Galvagni
Jun 28, 2018

There are exactly four distinct ways of getting to 3 by sequential spins: (1+1+1), (1+2), (2+1), (3).

Total probability= ( 1 3 ∗ 1 3 ∗ 1 3 ) + ( 1 3 ∗ 1 3 ) + ( 1 3 ∗ 1 3 ) + ( 1 3 ) (\frac{1}{3}*\frac{1}{3}*\frac{1}{3})+(\frac{1}{3}*\frac{1}{3})+(\frac{1}{3}*\frac{1}{3})+(\frac{1}{3})

= 1 27 + 1 9 + 1 9 + 1 3 = 16 27 \frac{1}{27}+\frac{1}{9}+\frac{1}{9}+\frac{1}{3}=\boxed{\frac{16}{27}}

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Very nice solution. Thank you!!!

A Former Brilliant Member - 2 years, 11 months ago

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Your solution is nice too, but more complicated than needed. The 16 in the numerator was suspicious and led me to try different numbers than 3. Interesting results.

Jeremy Galvagni - 2 years, 11 months ago

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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