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dedylja [7]
3 years ago
10

John and Lucy take turns rolling two dice. If John rolls a pair larger than or equal to 10 he wins and the game stops. If Lucy r

olls a pair strictly smaller than 10, she wins and the game stops. They keep rolling in turn until one of them wins. Suppose John rolls first. What is the probability that Lucy wins
Mathematics
1 answer:
grandymaker [24]3 years ago
4 0

Answer:

56.25%

Step-by-step explanation:

If John rolls first and Lucy rolls second, in order to find the probability that Lucy wins we need to multiply the probability that John's roll is less than 10 by the probability that Lucy's roll is less than 10. There are a total of 12 possible outcomes that can occur in a pair of dice, therefore John's probability of rolling less than a 10 would be \frac{9}{12} which would also be the same probability of Lucy rolling smaller than a 10. Now we simply multiply this probability by itself...

\frac{9}{12} * \frac{9}{12}  = \frac{81}{144} or 0.5625

We can multiply this decimal by 100 to get the percentage probability

0.5625 * 100 = 56.25%

The probability of Lucy winning the game is 56.25%

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159 as a percent = 15900%

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1.425 gallons/bottle.

<h3>Further explanation</h3>

<u>Given:</u>

  • Yasmine bought 6 gallons of apple juice.
  • After filling up 4 bottles of the same juice, she had 0.3 gallons of apple juice left.

<u>Question:</u>

What is the amount of apple juice in each container (or bottle)?

<u>The Process:</u>

Let the amount of apple juice in each bottle as X.

The two steps for obtaining X are as follows:

<u>Step-1:</u> the total amount of apple juice is the initial gallon amount subtracted by the remaining gallon amount.

\boxed{ \ 6 \ gallons - 0.3 \ gallons = 5.7 \ gallons \ }

<u>Step-2:</u> the total amount of apple juice divided by the number of bottles is the amount of apple juice in each bottle.

\boxed{ \ X = 5.7 \ gallons \div 4 \ bottles = \boxed{ \ 1.425 \ gallons/bottle \ } \ }

Let's also consider the following quick steps.

<u>Quick steps:</u>

\boxed{ \ X = \frac{(6 - 0.3) \ gallons}{4 \ bottles} = \boxed{ \ 1.425 \ gallons/bottle \ } \ }

Therefore, the amount of apple juice in each container (or bottle) is 1.425 gallons.

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