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2 years ago

You are rolling two dice at the same time. What is the probability of rolling a sum of 5 or 9?

2 answers:

8 0

You can get a 5 by rolling :
1 and 4
2 and 3
3 and 2
4 and 1

You can get a 9 by rolling :
3 and 6
4 and 5
5 and 4
6 and 3

There are 36 possible outcomes, hence your probability is $\frac{4\cdot2}{36}=\boxed{\frac29}$

oksian1 [2.3K]2 years ago

8 0

Answer:

Step-by-step explanation:

To find the probability we use the mutually exclusive probability formula P(A) + P(B). The probability of getting a sum of 5 is

1 /9

and the probability of getting a sum of 9 is

1 /9

. The sum is

2 /9

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Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.

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Answer:

Step-by-step explanation:

Hello, please consider the following.

$3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)$

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

$4^n+17$ is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so $4^k+17$ is divisible by 3

and we check what happens for k+1

$4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17$

$3\cdot 4^k$ is divisible by 3 and

$4^k+17$ is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that $4^n+17$ is divisible by 3 for all positive integers n.

Thanks

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