Coloured balls are distributed in four boxes as shown in the following table: A box is selected at random and then a ball is randomly drawn from the selected box. The colour of the ball is black, what is the probability that ball drawn is from the box III.

Question

Philoid · Accepted Answer

Given:

Box I has 3 Black, 4 White, 5 Red, 6 Blue balls

Box II has 2 Black, 2 White, 2 Red, 2 Blue balls

Box III has 1 Black, 2 White, 3 Red, 1 Blue balls

Box IV has 4 Black, 3 White, 1 Red, 5 Blue balls

Let us assume U₁, U₂, U₃, U₄ and A be the events as follows:

U₁ = choosing Box I

U₂ = choosing Box II

U₃ = choosing Box III

U₄ = choosing Box IV

A = choosing Black ball from box

We know that each urn is most likely to choose. So, probability of choosing a urn will be same for every Urn.

⇒

The Probability of choosing balls from each box differs from box to box and the probabilities are as follows:

⇒ P(A|U₁) = P(Choosing black ball from Box I)

⇒

⇒ P(A|U₂) = P(Choosing black ball from Box II)

⇒

⇒ P(A|U₃) = P(Choosing black ball from Box III)

⇒

⇒ P(A|U₃) = P(Choosing black ball from Box III)

⇒

Now we find

P(U₃|A) = P(The black ball is from BallIII)

Using Baye’s theorem:

⇒

∴ The required probability is .

Coloured balls are distributed in four boxes as shown in the following table:A box is selected at random and then a ball is randomly drawn from the selected box. The colour of the ball is black, what is the probability that ball drawn is from the box III.

Coloured balls are distributed in four boxes as shown in the following table:

A box is selected at random and then a ball is randomly drawn from the selected box. The colour of the ball is black, what is the probability that ball drawn is from the box III.