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andriy [413]
2 years ago
7

You have a biased coin for which p(h)=pp(h)=p. you toss the coin 2020 times. what is the probability that you observe 88 heads a

nd 1212 tails; you observe more than 88 heads and more than 88 tails?
Mathematics
1 answer:
Nat2105 [25]2 years ago
7 0
The question describes a binomial probability with p(h) = p, then p(t) = 1 - p and number of trials (n) = 20

The probability of a binomial distribution is given by

P(x)=\, ^nC_xp^x(1-p)^{n-x}

Part A:

The probability of observing 8 heads and 12 tails is given by:

P(8)=\, ^{20}C_8p^8(1-p)^{20-8}=\, ^{20}C_8p^8(1-p)^{12}



Part B:

<span>You observe more than 8 heads and more than 8 tails, when you observe 9 heads and 11 tails, 10 heads and 10 tails, and 11 heads and 9 tails.

Therefore, the probability of </span><span>observing more than 8 heads and more than 8 tails</span> is given by:

P(9)+P(10)+P(11) \\  \\ =\, ^{20}C_9p^9(1-p)^{20-9}+\, ^{20}C_{10}p^{10}(1-p)^{20-10}+\, ^{20}C_{11}p^{11}(1-p)^{20-11} \\  \\ =\, ^{20}C_9p^9(1-p)^{11}+\, ^{20}C_{10}p^{10}(1-p)^{10}+\, ^{20}C_{11}p^{11}(1-p)^{9}
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The researcher is interested to know if policy A (new) is more effective than policy B (old). Frame the hypothesis and describe
vesna_86 [32]

<u>Answer:</u>

<u>Null hypothesis: Policy B remains more effective than policy A.</u>

<u>Alternate hypothesis: Policy A is more effective than policy B.</u>

<u>Step-by-step explanation:</u>

Remember, a hypothesis is a  usually tentative (temporary until tested) assumption about two variables– independent and the dependent variable.

We have two types of hypothesis errors:

1. A type I error occurs when the null hypothesis (H0) is wrongly rejected.

That is, rejecting the assumption that policy B remains more effective than policy A when it is <em>actually true.</em>

2. A type II error occurs when the null hypothesis H0, is not rejected when it is actually false. That is, accepting the assumption that policy B remains more effective than policy A when it is <em>actually false.</em>

3 0
3 years ago
Kurt says factors and multiples are
maxonik [38]

<u>Step-by-step Explanation:</u>

<em>Before heading towards the solution, you need to make sure how multiple and factors are related to each other.</em>

<em>The multiple of a number could be obtained by multiply it with another number. </em>

For example, the first five multiples of 12 are 12, 24, 36, 48 and 60

  • 1 X 12 = 12
  • 2 X 12 = 24
  • 3 X 12 = 36
  • 4 X 12 = 48
  • 5 X 12 = 60

<em>Factors are the numbers that are multiplied to get a given number.</em>

For example,

  • 1 X 12 = 12
  • 2 X 12 = 24
  • 3 X 12 = 36

The factors of 12 are 1, 2, 3, 4, 6 and 12.

As division and multiplication can be used to find factors and multiples.

For example a whole number is a multiple of its factors.

Let w = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} be the set of even wholes numbers from 2 to 20.

As 2 is a factor of 20 because 20 ÷ 2 = 4

20 is a multiple of 2 because 2 X 10 = 20

So, in the same way, the equation 8 X 5 = 40 can be used to determine how factors and multiples are related.

Let the equation be

                                    8 X 5 = 40

8 is a factor of 40 because 8 X 5 = 40

40 is a multiple of 8 because 40 ÷ 5 = 8

<em>So, this is how factors and multiples are related to each other.</em>

<em />

<em>Keywords: factors, multiples, division, multiplication</em>

<em> Learn more about factors and multiples from brainly.com/question/596356</em>

<em> #learnwithBrainly</em>

4 0
2 years ago
Two number cubes are rolled. What is the probability that the sum of the numbers rolled is either 4 or 8?
sveticcg [70]

There are 6 numbers on each die.

The total number of out comes is 6 x 6 = 36.


To get a sum of 4, the combinations are: 1 & 3, 2 & 2 or 3 & 1.

To get a sum of 8, the combinations are: 1 & 7, 2 & 6, 3 & 5, 4 & 4, 7 & 1, 6 & 2, 5 & 3


The total of those combinations are:  3  + 7 = 10 total combinations of a sum of either 4 or 8.


The probability of either is 10/36, which can be reduced to 5/18.

8 0
2 years ago
Camille stopped at the grocery store to buy milk. While at the store, she spotted cans of soup on sale for $2.25 each. If the mi
Mrrafil [7]
$2.25x+$3.50=$35

so, $35-$3.50=$31.50

Then you divide $31.50 by $2.25

That equals 14

So, x=14
8 0
3 years ago
Can u please help me with this question
zaharov [31]

Answer:

D

its the big clix

6 0
3 years ago
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