Mathematics, 08.10.2020 17:01 yfnal3x

The Reviews editor for a certain scientific journal decides whether the review for any particular book should be short (1–2 pages), medium (3–4 pages), or long (5–6 pages). Data on recent reviews indicates that 50% of them are short, 30% are medium, and the other 20% are long. Reviews are submitted in either Word or LaTeX. For short reviews, 70% are in Word, whereas 50% of medium reviews are in Word and 30% of long reviews are in Word. Suppose a recent review is randomly selected.(a) What is the probability that the selected review was submitted in Word format?(b) If the selected review was submitted in Word format, what are the posterior probabilities of it being short, medium, or long? (Round your answers to three decimal places.)shortmediumlong

Answers: 1

Show answers

Answers

Answer from: isabellesolisss5217

The probability that the selected review was submitted in Word format is 0.56.

Step-by-step explanation:

We are given that Data on recent reviews indicates that 50% of them are short, 30% are medium, and the other 20% are long. Reviews are submitted in either Word or LaTeX. For short reviews, 70% are in Word, whereas 50% of medium reviews are in Word and 30% of long reviews are in Word.

Let the probability that there are short reviews = P(S) = 0.50

The probability that there are medium reviews = P(M) = 0.30

The probability that there are long reviews = P(L) = 0.20

Let W = event that the reviews are submitted in either Word or LaTeX

So, the probability that short reviews are submitted in Word = P(W/S) = 0.70

The probability that medium reviews are submitted in Word = P(W/M) = 0.50

The probability that long reviews are submitted in Word = P(W/L) = 0.30

(a) The probability that the selected review was submitted in Word format is given by = P(W)

P(W) = P(S) $\times$ P(W/S) + P(M) $\times$ P(W/M) + P(L) $\times$ P(W/L)

= (0.50 $\times$ 0.70) + (0.30 $\times$ 0.50) + (0.20 $\times$ 0.30)

= 0.35 + 0.15 + 0.06

= 0.56

Hence, the probability that the selected review was submitted in Word format is 0.56.

(b) Now, if the selected review was submitted in Word format, the posterior probabilities of it being short is given by = P(S/W)

P(S/W) = $\frac{P(S) \times P(W/S)}{P(S) \times P(W/S)+P(M) \times P(W/M)+P(L) \times P(W/L)}$

= $\frac{0.50\times 0.70}{0.50\times 0.70+0.30\times 0.50+0.20\times 0.30}$

= $\frac{0.35}{0.56}$ = 0.625

Similarly, if the selected review was submitted in Word format, the posterior probabilities of it being medium is given by = P(M/W)

P(M/W) = $\frac{P(M) \times P(W/M)}{P(S) \times P(W/S)+P(M) \times P(W/M)+P(L) \times P(W/L)}$

= $\frac{0.30\times 0.50}{0.50\times 0.70+0.30\times 0.50+0.20\times 0.30}$

= $\frac{0.15}{0.56}$ = 0.268

Also, if the selected review was submitted in Word format, the posterior probabilities of it being long is given by = P(L/W)

P(L/W) = $\frac{P(L) \times P(W/L)}{P(S) \times P(W/S)+P(M) \times P(W/M)+P(L) \times P(W/L)}$

= $\frac{0.20\times 0.30}{0.50\times 0.70+0.30\times 0.50+0.20\times 0.30}$

= $\frac{0.06}{0.56}$ = 0.107.

Answer from: Quest

$x \geqslant - 6$

step-by-step explanation:

it's is b

() solve the inequality below for x: -4x-11< 13

Answer from: Quest

17 x 256=4352

sorry if this is wrong, i'm new.

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 17:30, Jerrikasmith28

Based on the figures as marked, /\rqs = —

Answers: 1

continue

Mathematics, 21.06.2019 17:30, amiechap12

Let f(x) = x+3 and g(x) = 1/x the graph of (fog)(x) is shown below what is the range of (fog)(x)?

Answers: 2

continue

Mathematics, 21.06.2019 20:00, 12bluestone

Someone answer asap for ! a discount store’s prices are 25% lower than department store prices. the function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars. if the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. the function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars. create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month. d(c(x)) =

Answers: 1

continue

Mathematics, 21.06.2019 22:00, malikxyo224

Rewrite so the subject can be y in the formula d=m-y/y+n

Answers: 1

continue

You know the right answer?

The Reviews editor for a certain scientific journal decides whether the review for any particular bo...