Question

Urn I contains five red chips and four white chips; urn II contains four red and five white chips. Two chips are drawn simultaneously from urn I and placed into urn II. Then a single chip is drawn from urn II. What is the probability that the chip drawn from urn II is white?

Answer 1

Answer: Our required probability is 0.56.

Step-by-step explanation:

Since we have given that

In urn I :

Number of red chips = 5

Number of white chips = 4

In urn 2 :

Number of red chips = 4

Number of white chips = 5

Two chips are drawn simultaneously from urn I and placed into urn II. Then a single chip is drawn from urn II.

Probability that the chip drawn from urn II is white is given by

P(E₁) = $\dfrac{1}{2}$ = P(E₂)

P(W|E₁) = $\dfrac{4}{9}$

P(W|E₂) = $\dfrac{5}{9}$

So, by "Bayes theorem ", we get that

$P(E_2|W)=\dfrac{0.5\times \dfrac{5}{9}}{0.5\times \dfrac{4}{9}+0.5\times \dfrac{5}{9}}\\\\P(E_2|W)=\dfrac{5}{9}=0.56$

Hence, our required probability is 0.56.