An agricultural research establishment grows vegetable and grades, each one as e

Question

An agricultural research establishment grows vegetable and grades, each one as either good or bad for its taste, good or bad for its size, and good or bad for its appearance. Overall 78% of the vegetables have a good taste. However, only 69% of the vegetables have both a good taste and a good size. Also 5% of the vegetables have both a good taste and a good appearance, but a bad size. Finally, 84% of the vegetables have either a good size or a good appearance. (a) If a vegetable has a good taste, what is the probability that it also has a good size? (b) If a vegetable has a bad size and bad appearance, what is the probability that it has a good taste?

Explanation / Answer

From the given information we have,

P(good taste) = 0.78

P(good taste and good size) = 0.69

P(good taste and good appearance and bad size) = 0.05

P(good size or good appearance) = 0.84

(a)

Here we need to find the probability P(good size | good taste) .

So,

P(good size | good taste) = P(good taste and good size) / P(good taste) = 0.69 / 0.78 = 0.8846

(b)

Need to find the probability P(good taste | bad size and bad appearance).

By the complement rule,

P(bad size and bad appearance) = 1- P(good size or good appearance) = 1 - 0.84 = 0.16

P(good taste and bad appearance and bad size) = P(good taste) - P(good taste and good size) - P(good taste and good appearance and bad size) = 0.78- 0.69 - 0.05 = 0.04

And

P(bad size and bad appearance and good taste) =P(good taste and bad appearance and bad size) / P(bad size and bad appearance) = 0.04 /0.16 = 0.25

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.