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Anarel [89]
2 years ago
6

Roll two 6-sided dice and examine their sum.

Mathematics
1 answer:
Karo-lina-s [1.5K]2 years ago
5 0
<span>a) How long will it take to roll "snake-eyes" (a pair of ones)?
P(a pair of ones) = 1/36
Therefore, it takes 36 rolls to roll "snake-eyes".

b) What is the probability of rolling a sum of 7 on the first roll?
P(a sum of 7) = 6/36 = 1/6
P(a sum of 7 on the first roll) = 1/6

c) What is the probability of rolling a sum of 7 on the fourth roll?
P(a sum of 7 on the fourth roll) = </span><span><span>(5/6)^3 * 1/6 = 125/1296</span>

d) What is the probability of rolling a sum of 7 by the fourth roll?
P(a sum of 7 by the fourth roll) = 1/6 + (5/6) * 1/6 + (5/6)^2 * 1/6 + (5/6)^3 * 1/6 = 1/6 + 5/36 + 25/216 + 125/1296 = 671/1296

e) What is the probability of it takin</span>g more than 10 rolls to roll the sum of 7?
P(more than 10 rolls to roll the sum of 7) = 1 - P(no sum of 7 in the first 10 rolls) = 1 - (5/6)^10 = 1 - 0.1615 = 0.8385

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AleksAgata [21]
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6 0
2 years ago
What sampling method is used in the following examples. Is the method biased or not?
Romashka-Z-Leto [24]

Answers:

  • a) Stratified random sampling, or simply stratified sampling. Each group individually is known as a stratum. The plural is strata. The key here is that each stratum is sampled, though we don't pick everyone from every stratum. We randomly select from each unit to have them represent their unit. Think of it like house of representative members that go to congress. We have members from every state, but  Be sure not to mix this up with cluster sampling. Cluster sampling is where we break the population into groups or clusters, then we randomly select a few clusters in which every individual from those clusters is part of the sample.
  • b) Simple random sampling (SRS). This is exactly what it sounds like. We're randomly generating numbers to help determine who gets selected. Think of it like a lottery. A computer is useful to make sure this process is quick, efficient and unbiased as possible. Though numbers in a box or a hat work just as well.

For each of the methods mentioned, they aren't biased since they have randomness built into their processes.

7 0
3 years ago
(m 5/6) (m1/6) ^7 = m^x
nadezda [96]

Answer:

x = 2

Step-by-step explanation:

Here, we want to find the value of x

(m^5/6)(m^1/6)^7 = m^x

= (m^5/6)(m^7/6) = m^x

Using the law of indices for power multiplication

m^(5/6 + 7/6) = m^x

m^(12/6) = m^x

m^2 = m^x

we simply equate the powers in this case since the base are equal

Thus we have

x = 2

3 0
2 years ago
Do modern scientists believe that protons and nuetrons are not made of smaller particles
anyanavicka [17]

Answer: Thus, protons and neutrons are no more indivisible than atoms are; indeed, they contain still smaller particles, which are called quarks. Quarks are as small as or smaller than physicists can measure.

Step-by-step explanation:

4 0
2 years ago
Trent writes p^2 + 30 = (p + 30)(p + 0)<br><br> Do you agree with Trent? Explain why
Bingel [31]

Answer:

Statement expressed by Trent is RIGHT.

(p^2 + 30) = (p+30)(p +0)

Step-by-step explanation:

Here, the given expression is:

( to show)   :  (p^2 + 30) = (p+30)(p +0)

Now, as we know by DISTRIBUTIVE PROPERTY:

A (B + C)  = AB  + AC

Consider the RHS of the expression:

(p +30)(p+0)  =  (p +30)(p)   ............  ( a + 0 = a for all a)

Simplifying (p +30)(p) by distributive property, we get:

(p +30)(p)   = p(p) + 30(p) \\= p^2 + 30p\\\implies (p+30)(p+0)  =  p^2 + 30p

⇒ Left side  = Right side

Hence,  statement expressed by Trent is RIGHT.

8 0
2 years ago
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