Question

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?

Answer 1

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

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

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

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