Question

Asked Oct 20, 2019

The prior probabilities for events
*B* given

A_{1}, A_{2}, and A_{3}

are
P(A_{1}) = 0.20,

P(A_{2}) = 0.30,

and
P(A_{3}) = 0.50.

The conditional probabilities of event A_{1},

A_{2},

and
A_{3}

are
P(B | A_{1}) = 0.50,

P(B | A_{2}) = 0.30,

and
P(B | A_{3}) = 0.40.

(Assume that
A_{1}, A_{2}, and A_{3}

are mutually exclusive events whose union is the entire sample space.)(a)

Compute

P(B ∩ A_{1}), P(B ∩ A_{2}), and P(B ∩ A_{3}).

P(B ∩ A_{1})

=
P(B ∩ A_{2})

=
P(B ∩ A_{3})

=(b)

Apply Bayes' theorem,

P(A_{i} | B) =

,

to compute the posterior probability
P(A_{i})P(B | A_{i}) |

P(A_{1})P(B | A_{1}) + P(A_{2})P(B | A_{2}) + + P(A_{n})P(B | A_{n}) |

P(A_{2} | B).

(Round your answer to two decimal places.)(c)

Use the tabular approach to applying Bayes' theorem to compute

P(A_{1} | B),

P(A_{2} | B),

and
P(A_{3} | B).

(Round your answers to two decimal places.)Events |
P(A
_{i}) |
P(B | A
_{i}) |
P(A
_{i} ∩ B) |
P(A
_{i} | B) |
---|---|---|---|---|

A
_{1} |
0.20 | 0.50 | ||

A
_{2} |
0.30 | 0.30 | ||

A
_{3} |
0.50 | 0.40 | ||

1.00 | 1.00 |

Step 1

(a)

From the given information, *P*(*A*_{1})=0.20, *P*(*A*_{2})=0.30, *P*(*A*_{3})=0.50, *P*(*B*|*A*_{1})=0.5, *P*(*B*|*A*_{2})=0.30 and *P*(*B*|*A*_{3})=0.40.

Step 2

(b)

The value of *P*(*A*2|*B*) is **0.23** and it is calculated...

Tagged in

Q: Scores on a statistics final in a large class were normally distributed with a mean of 70 and a stan...

A: a) According to the provided information, it is given µ = 70 and σ = 7The probability that one rando...

Q: An investigator conducts a study to investigate whether there is a difference in mean PEF in childre...

A: Introduction:The 100 (1 – α) % confidence interval for the population mean, μ, for given sample stan...

Q: The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of...

A: Given information:Sample size (n) = 250The number of hours cars are parked and the amount they are c...

Q: Would it be unusual for an data value to be more extreme than 4.76 standard deviations from the mean...

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: 6.46 Jury duty The juror pool for the upcoming murder ti. of a celebrity actor contains the names of...

A: a. Conditions for Binomial Distribution:Conditions for Binomial Distribution are as follows:Each tri...

Q: Data Table The table gives percentages for results of flipping seven coins. Complete parts (a) throu...

A: Given data

Q: Consider a Poisson distribution with μ 3. Write the appropriate Poisson probability function. ...

A: It is given that µ = 3.

Q: Suppose the correlation between height and weight for adults is +0.40. What proportion (or percent) ...

A: It is given that the correlation between height and weight is 0.40.

Q: Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from ...

A: The provided regression equation is,