Let\'s calculate the probability of winning the California Daily 3 lottery (ther

Question

Let's calculate the probability of winning the California Daily 3 lottery (there is no lottery in NC).   In this lottery, you pick three numbers between 0 and 9. You can pick the same number multiple times, e.g. you can pick 7-7-5 or 7-7-7.   You choose to play one of three ways: (i) "straight", which means you win if you pick the three numbers in the exact order that they are drawn, (ii) "box", which means you win if you pick the three numbers correctly in any order, (iii) "straight/box", which means you win if you pick three numbers that win either the straight or the box styles. Prizes for each style are determined from the numbers of people who play the game in that style.

For example, say you pick 7-7-5. If the drawn numbers are 7-7-5, you'd win in all three styles of play. If the drawn numbers are 7-5-7, you win the box and straight/box style, but do not win the straight style. If the numbers are 2-0-5, you win nothing.

Problem:

Say you pick 1-2-3. What is the probability of winning straight style?   What is the probability of winning box style? What is the probability of winning straight/box style?

Explanation / Answer

1-2-3 can be obtained in only one way in the experiment of selecting 3 numbers from 0 to 9.

Any 3 numbers can be obtained from 0-9 in 10*10*10=1000 ways.

Probability of winning straight style:

1/1000.

Probability of winning box style:

You win in box style if you pick 1-3-2 or 2-1-3 or 2-3-1 or 3-1-2 or 3-2-1.

So probability of winning box style: 5/1000

Probability of winning straight/box style:

You win straight/ box style if you choose 1-2-3 or 1-3-2 or 2-1-3 or 2-3-1 or 3-1-2 or 3-2-1

So, probability of winning straight/box style. =6/1000

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