Question

In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from $1$ to $10$, and one SuperBall is drawn (at random) from ten red balls numbered from $11$ to $20$. When you buy a ticket, you choose three numbers from $1$ to $10,$ and one number from $11$ to $20$.

If the numbers on your ticket match the three white balls and the red SuperBall, then you win the jackpot. (You don't need to match the white balls in order). What is the probability that you win the jackpot?

Answer 1

This question is solved using probability concepts.

• A probability is given by the number of desired outcomes divided by the number of total outcomes.
• The order in which the balls are chosen don't matter, which means that the combinations formula is used to find the number of outcomes.

Doing this, we get that:

$\frac{1}{1200}$ probability that you win the jackpot.

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Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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Total outcomes:

• 3 white from a set of 10(numbered from $1 to $10).
• 1 red from a set of 10(numbered from $11 to $20).

Thus:

$T = C_{10,3}C_{10,1} = \frac{10!}{7!3!} \times \frac{10!}{1!9!} = 120 \times 10 = 1200$

Desired outcomes:

The correct balls, order does not matter, so only one outcome, that is, $D = 1$

What is the probability that you win the jackpot?

$p = \frac{D}{T} = \frac{1}{1200}$

$\frac{1}{1200}$ probability that you win the jackpot.

A similar question is given at https://brainly.com/question/23966554

Answer 2

Answer:

6/7200=1/1200

Step-by-step explanation:

[3! ways to arrange the three white balls] over [10x9x8 ways to pick three white balls and 10 ways to pick a red]  =3x2x1/10x9x8x10=6/72x100=6/7200=1/1200

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