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forsale [732]
3 years ago
6

Morgan is playing a board game that requires three standard dice to be thrown at one time. Each die has six sides, with one of t

he numbers 1 through 6 on each side. She has one throw of the dice left, and she needs a 17 to win the game. What is the probability that Morgan wins the game (order matters)?
Mathematics
1 answer:
kati45 [8]3 years ago
3 0

Question:

Morgan is playing a board game that requires three standard dice to be thrown at one time. Each die has six sides, with one of the numbers 1 through 6 on each side. She has one throw of the dice left, and she needs a 17 to win the game. What is the probability that Morgan wins the game (order matters)?

Answer:

1/72

Step-by-step explanation:

<em>Morgan can roll a 17 in 3 different ways. The first way is if the first die comes up 5, the second die comes up 6, and the third die comes up 6. The second way is if the first die comes up 6, the second die comes up 5, and the third die comes up 6. The third way is if the first die comes up 6, the second die comes up 6, and the third die comes up 5. For each way, the probability of it occurring is  1/6 x 1/6 x 1/6 = 1/216. Therefore, since there are 3 different ways to roll a 17, the probability that Morgan rolls a 17 and wins the game is  1/216 + 1/216 + 1/216 = 3/216 = 1/72</em>


<em>I had this same question on my test!</em>


<em>Hope this helped! Good Luck! ~LILZ</em>


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Using the hypergeometric distribution, it is found that there is a 0.4286 = 42.86% probability of getting 2 of the same colour.

The marbles are chosen without replacement, hence the <em>hypergeometric </em>distribution is used to solve this question.

<h3>What is the hypergeometric distribution formula?</h3>

The formula is:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}

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

The parameters are:

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  • N is the size of the population.
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In this problem:

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  • Of those, 3 are blue, hence k = 3.
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The probability of getting 2 of the same colour is the sum of P(X = 0), which is both red, with P(X = 2), which is both blue, then:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}

P(X = 0) = h(0,7,2,3) = \frac{C_{3,0}C_{4,2}}{C_{7,2}} = 0.2857

P(X = 2) = h(2,7,2,3) = \frac{C_{3,2}C_{4,0}}{C_{7,2}} = 0.1429

Hence:

p = P(X = 0) + P(X = 2) = 0.2857 + 0.1429 = 0.4286

0.4286 = 42.86% probability of getting 2 of the same colour.

You can learn more about the hypergeometric distribution at brainly.com/question/4818951

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