Use bayes theorem to solve this problem, a paper bag contains two red balls and one blue ball. A plastic bag contains three blue

Question

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Use bayes theorem to solve this problem, a paper bag contains two red balls and one blue ball. A plastic bag contains three blue

balls and one red ball. A coin is tossed. If it falls heads up, the paper bag is selected and a ball is drawn. If the coin falls tails up, the plastic bag is selected and a ball is drawn. If a red ball is selected what is the probability that it came from the paper bag?

Mathematics

1 answer:

Basile [38] · Answer 1 · 2020-11-22T19:51:17+03:00

Answer: $\frac{8}{11}$

Step-by-step explanation:

Given

Probability of selecting Paper bag is equivalent to getting a head in coin i.e. 0.5 and probability of selecting Plastic bag is equivalent to getting a tail in coin i.e. 0.5

Probability of getting a red ball from Paper bag $=\frac{2}{3}$

Probability of getting a red ball from Plastic bag $=\frac{1}{4}$

If a red ball is selected Probability that it came from the paper bag

$P=P(Red\ ball\ from\ paper\ bag|Red\ ball)$

$P=\frac{\frac{1}{2}\times \frac{2}{3}}{\frac{1}{2}\times \frac{2}{3}+\frac{1}{2}\times \frac{1}{4}}$

$P=\frac{2}{2+\frac{3}{4}}=\frac{8}{11}$