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BlackZzzverrR [31]
3 years ago
11

Two dice are rolled. Use the complement rule to find that the probability that the sum of the dice is less than 10.

Mathematics
1 answer:
Katarina [22]3 years ago
6 0

Answer:

\dfrac{5}{6}

Step-by-step explanation:

When two dice are rolled, the sample space is

\begin{array}{cccccc}(1,1)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6)\\(2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6)\\(3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6)\\(4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6)\\(5,1)&(5,2)&(5,3)&(5,4)&(5,5)&(5,6)\\(6,1)&(6,2)&(6,3)&(6,4)&(6,5)&(6,6)\end{array}

In total, 36 outcomes

First, find the probability that the sum is 10 or greater:

All favorable outcomes

10: (4,6),\ (5,5),\ (6,4)

11: (5,6),\ (6,5)

12: (6,6)

In total, 6 outcomes.

The probability that the sum is 10 or greater is

P(A)=\dfrac{6}{36}=\dfrac{1}{6}

Use the complement rule to find that the probability that the sum of the dice is less than 10:

P(A^C)=1-P(A)=1-\dfrac{1}{6}=\dfrac{5}{6}

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Alisiya [41]

The time taken to reach train from Zurich to Paris is 8 hours 52 minutes.

Step-by-step explanation:

          The given is,

                     Train leaves Zurich at 22:40

                     Train arrives Paris at 07:32

Step:1

          Time taken to reach from zurich to paris,

                            = Train leaves at Zurich - Train arrives at Paris

                            = 22:40 - 07:32

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Step:2  

         Time taken by train to reach from zurich to paris in minutes,

                           = 8.52 hours

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Result:

        The time taken to reach train from Zurich to Paris is 8 hours 52 minutes, if a train leaves Zurich at 2240 and arrives in Paris at 0732.

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Step-by-step explanation:

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