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Conditional Probability & Bayes' Theorem · Question 78 of 125

Question 78

EasyOriginal question

A coin is tossed. On a head, a ball is drawn from urn A (2 red, 3 blue); on a tail, from urn B (4 red, 1 blue). What is the probability that the ball is red?

Options for question 78

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. P(R)=12×25+12×45P(R) = \frac{1}{2} \times \frac{2}{5} + \frac{1}{2} \times \frac{4}{5}.

  2. 15+25=35\frac{1}{5} + \frac{2}{5} = \frac{3}{5}.

Worth noting

25\frac{2}{5} uses urn A only, as if the coin always showed a head.

Concept
The theorem of total probability
Typical time
60 s
Your time
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The rule this testsThe theorem of total probability
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