EduFarming
Your list · 0हिं

Type at least two letters. Press Esc to close.

↑↓ navigate↵ openTAB cycle filter

Conditional Probability & Bayes' Theorem · Question 98 of 125

Question 98

HardOriginal question

A shop's seeds come from two growers, X and Y. 80% of X's seeds and 30% of Y's seeds sprout, and 50% of all the shop's seeds sprout. What is the probability that a seed picked at random came from X?

Options for question 98

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. With p=P(X)p = P(X), total probability gives 0.8p+0.3(1−p)=0.50.8p + 0.3(1 - p) = 0.5.

  2. 0.5p=0.20.5p = 0.2, so p=0.4p = 0.4.

Worth noting

0.625 is 0.50.8\frac{0.5}{0.8}, which leaves out Y's seeds, though they sprout too.

Concept
Working back through total probability
Typical time
120 s
Your time
—
The rule this testsThe theorem of total probability
Practise this chapter →

Ten questions from Conditional Probability & Bayes' Theorem, at your own pace.

Practise this chapter →

Ten questions from Conditional Probability & Bayes' Theorem, at your own pace.

Practise this chapterAll 125 questions in Conditional Probability & Bayes' TheoremRevise the notes for Conditional Probability & Bayes' Theorem