Can someone help me find this answer plz

In answering on a multiple choice test, a student either know the answer or guesses. Let p be the probability that the students

LenaWriter [7]

Answer:

$P(A_{1}|B ) =\frac{mp}{1+p(m-1)}$

Step-by-step explanation:

For mutually exclusive events as A1, A2, A3, etc, Bayes' theorem states:

$P(A|B)= \frac{P(B|A)P(A)}{P(B)}$

P(A|B) is a conditional probability: the likelihood of event A occurring given that B is true.

P(B|A) is a conditional probability: the likelihood of event B occurring given that A is true.

P(A) is the probability that A occurs

P(B) is the probability that B occurs

For this problem:

A1 is the probability that the student knows the answer

A2 is the probability that the student guesses the answer

B is the probability that the student answer correctly

$P(A_{1})=p \\P(A_{2})=1-p \\P(B|A_{1})=1 \\P(B|A_{2})=\frac{1}{m} \\P(B)= P(A_{1})P(B|A_{1}) + P(A_{2})P(B|A_{2})= p+\frac{1-p}{m} \\$

P(B|A₁) means the probability that the answer is correct when he knew the answer

P(B|A₂) means the probability that the answer is correct when he guessed the answer

P(A₁|B) means the probability that he knew the answer when the answer was correct

Replacing everything in the Bayes' theorem you get:

$P(A_{1}|B)= \frac{P(B|A_{1})P(A_{1})}{P(B)}=\frac{(1)(p)}{p+\frac{1-p}{m}} =\frac{mp}{mp+1-p} =\frac{mp}{1+p(m-1)}$

5 0

3 years ago

The distribution of prices for home sales in a certain New Jersey county is skewed to the right with a mean of $290,000 and a st

I am Lyosha [343]

Answer:

The probability that the mean of the sample is greater than $325,000

$P( X > 3,25,000) = P( Z >2.413) = 0.008$

Step-by-step explanation:

Step(i):-

Given the mean of the Population( )= $290,000

Standard deviation of the Population = $145,000

Given the size of the sample 'n' = 100

Given 'X⁻' be a random variable in Normal distribution

Let X⁻ = 325,000

$Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{325000-290000}{\frac{145000}{\sqrt{100} } } = 2.413$

Step(ii):-

The probability that the mean of the sample is greater than $325,000

$P( X > 3,25,000) = P( Z >2.413)$

= 0.5 - A(2.413)

= 0.5 - 0.4920

= 0.008

Final answer:-

The probability that the mean of the sample is greater than $325,000

$P( X > 3,25,000) = P( Z >2.413) = 0.008$

6 0

3 years ago

HELP FIRST GET BRAINLLEST Which of the statements below are true? Select all that apply. A) Tom's friends are taller than Sam's

Vadim26 [7]

Answer:

Step-by-step explanation:

c

6 0

3 years ago

Read 2 more answers

Winston bought an encyclopedia priced at $42. Shipping and handling cost anadditional 30% of the price. What was the total cost

Sergio039 [100]

Answer:

42.3

Sorry I haven't been answering your questions I'm just behind on homework.

3 0

3 years ago

3. How many 1/8's are in 1 1/4?

Murrr4er [49]

Answer:

10

Step-by-step explanation:

There are two 1/8 in one 1/4. There are eight 1/8 in 1. 8/8 + 1/8 + 1/8 = ten 1/8.

3 0

3 years ago