Bowling a Perfect 300!

Probability Level 2

In the game of Bowling , let's say a pro bowler has a $70$ % chance of bowling a strike (knocking over all ten pins in one try).

His odds of bowling a perfect 300 (12 strikes in a row) is $x$ %. What is $x$ ?

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The answer is 1.38.

1 solution

Brack Harmon
Aug 10, 2018

The probability of getting a strike, $p$ , is raised to the number of $n$ strikes.

We get:

$P_{n} = p^{n}$

$P_{12} = .7 ^{ 12 }$ ≈ $\color{#3D99F6}{1.38}$ %

A more accurate way to compute the odds of a perfect 300 game is to consider each frame as an ordered-pair (x,y) where:

x = pins on first roll, y = pins on second roll, x + y = 10, x, y = {0, 1, 2, ... , 10}

If you write out all of the possible ordered-pairs, there are 66 possible outcomes. A strike is the pair (10,0) in which a bowler has 1/66 chance of rolling. The true odds of obtaining a perfect 300 (regardless of ability) computes to (1/66)^12 = 1.463 x 10^-22. You'd actually have a better chance of winning a Lottery!!

In nearly 40 years of bowling myself, I've only pulled off ONE 300 with my own gear.....I'll definitely take it :)

tom engelsman - 6 months, 2 weeks ago

Bowling a Perfect 300!

The answer is 1.38.

1 solution

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