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padilas [110]
3 years ago
8

You are given an unfair coin (i.e. a coin where the probability of it landing on either side is NOT 1/21/2) and told that the pr

obability of getting at least one tails in three tosses of said coin is 26/2726/27. The probability of getting heads in one toss of the unfair coin can be expressed in the form M/NM/N, where MM and NN are relatively prime positive integers (i.e. their greatest common divisor is 1). Compute M + NM+N
Mathematics
1 answer:
andrey2020 [161]3 years ago
6 0

Here we have a problem of probability, we will find that the probability of landing in heads is M/N = 1/3, then we have:

M + N = 1 + 3 = 4.

Let's see how we got that:

Let's define:

p = probability of landing on tails

q = probability of landing on heads.

The probability of getting at least one tails in 3 tosses is 26/27

This means that the probability of not getting tails in the 3 tosses is:

P = 1 - 26/27 = 1/27

And the case where you do not get any tails in the 3 tosses, means that in all the 3 tosses you got heads.

The probability of getting 3 heads in a row is:

P = q^3 = 1/27

Solving for q, we get:

q = ∛(1/27) = 1/3

Now we want to express q = M/N = 1/3

then we have:

M = 1

N = 3

Now we want to compute M + N = 1 + 3 = 4

If you want to learn more about probability, you can read:

brainly.com/question/24369877

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According to a​ survey, 60 ​% of the residents of a city oppose a downtown casino. Of these 60 ​% about 8 out of 10 strongly opp
katrin [286]

Answer:

(a) 0.48

(b) 0.20

(c) it is not unusual for a radomly selected resident to oppose the casino and strongly oppose the​ casino.

Step-by-step explanation:

​(a) Find the probability that a randomly selected resident opposes the casino and strongly opposes the casino. ​

The probability that a radomly selected resident opposes the casino and strongly opposes the cassino is the product of the two probabilities, that a resident opposes the casino and that it strongly opposes the casino (once it is in the first group) as it is shown below.

Use this notation:

  • Probability that a radomly selected resident opposes the casino: P(A)

  • Probability that a resident who opposes the casino strongly opposes it: P(B/A), because it is the probability of event B given the event A

i) Determine the <em>probability that a radomly selected resident opposes the casino</em>, P(A)

Probability = number of favorable outcomes / number of possible outcomes

  • P(A) is <em>given as 60%</em>, which in decimal form is 0.60

ii) Next, determine,the <em>probability that a resident who opposes the casino strongly opposes it</em>, P(B/A):

  • It is given as 8 out of 10 ⇒ P(B/A) = 8/10

iii) You want the probability of both events, which is the joint probability or  intersection: P(A∩B).

So, you can use the definition of conditional probability:

  • P(B/A) = P(A∩B) / P(A)

iv) From which you can solve for P(A∩B)

  • P(A∩B) = P(B/A)×P(A) =  (8/10)×(0.60) = 0.48

(b) Find the probability that a randomly selected resident who opposes the casino does not strongly oppose the casino.

In this case, you just want the complement of the probability that <em>a radomly selected resident who opposes the casino does strongly oppose the casino</em>, which is 1 - P(B/A) = 1 - 8/10 = 1 - 0.8 = 0.2.

​(c) Would it be unusual for a randomly selected resident to oppose the casino and strongly oppose the​ casino?

You are being asked about the joint probability (PA∩B), which you found in the part (a) and it is 0.48.

That is almost 0.50 or half of the population, so you conclude it is not unusual for a radomly selected resident to oppose the casino and strongly oppose the​ casino.

8 0
3 years ago
You are repairing a fence and have 7.9 metres of wood. You need 10 metres.
iren2701 [21]
4 you will have 2.1 meters of wood left over
5 0
3 years ago
You open a business selling school supplies and tutoring sessions. In your first week, you had $9,000 in sales. You ran a promot
vaieri [72.5K]

Answer: total net sales = $7950

Step-by-step explanation:

The formula for determining total net sales is expressed as

total net sales = Gross sales - (sales returns + allowances + discount)

Gross sales means total sales.

From the information given,

Gross sales = $9000

Discounts = $900

Returns = $150

Allowances = 0(this is because it was not given)

Therefore,

total net sales = 9000 - (900 + 150)

= 9000 - 1050

total net sales = $7950

3 0
3 years ago
Find the magnitude of WX for W(-2, 8, -3) and X(1, 4, -1)
zheka24 [161]

The magnitude of WX is  \sqrt{29}  ⇒ c

Step-by-step explanation:

The magnitude of XY (its length) where,

  • X=(x_{1},y_{1},z_{1})
  • Y=(x_{2},y_{2},z_{2})

is IXYI = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}

∵ W = (-2 , 8 , -3)

∵ X = (1 , 4 , -1)

- To find the magnitude of WX use the formula above

∴ x_{1} = -2 and x_{2} = 1

∴ y_{1} = 8 and y_{2} = 4

∴ z_{1} = -3 and z_{2] = -1

- Substitute these values in the rule above

∵ IWXI = \sqrt{(1--2)^{2}+(4-8)^{2}+(-1--3)^{2}}=\sqrt{9+16+4}

∴ IWXI = \sqrt{29}

The magnitude of WX is  \sqrt{29}

Learn more:

You can learn more about the position of an object in brainly.com/question/10940255

#LearnwithBrainly

8 0
3 years ago
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Super easy to get pointsss!!! HELPPPP
jeyben [28]

Answer:

3x3x12= volume of large prism= 108

1x1x12= volume of hole= 12

(Volume of prism)-(volume of hole)= 96

Step-by-step explanation:

8 0
4 years ago
Read 2 more answers
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