Question

1. Box #1 contains 4 red chips and 1 white chip. Box #2 contains 3 red, 1 black and 6 white chips. The experiment consists of randomly picking a box, then randomly picking a chip from it. Find the probability that: (a) A red chip is drawn from Box #1: ___________________________________ (b) A red chip is drawn, given that Box #1 was picked: ________________________________ (c) Box #1 was picked, given that the chip is black: _____________________________

Answer 1

Box #1 contains 4 red chips and 1 white chips.

Box #2 contains 3 red, 1 black and 6 white chips.

The experiment consists of randomly picking a box, then randomly picking a chip from it

Tree diagram :

P(Box1)=P(Box2) = 1/2

P( Red chip | Box1 ) = 4/5

P( white chip | Box1 ) = 1/5

P( Red chip | Box2 ) = 3/10

P( white chip | Box2 ) = 6/10

P( black chip | Box2 ) = 1/10

a)

We have to find probability that a red chip is drawn from Box #1.

P( Red chip is drawn from Box #1 ) = P( Box1)*P( Red chip | Box1 )

P( Red chip is drawn from Box #1 ) = (1/2)*(4/5)

P( Red chip is drawn from Box #1 ) = 4/10 = 0.4

b)

We have to find probability that red chip is drawn, given that Box1 was picked.

In Notation we have to find P( Red chip | Box1 )

P( Red chip | Box1 ) = 4/5 = 0.8 From tree diagram }

c)

We have to find probability that Box1 was picked, given that the chip is black.

There is no black chips in Box1.

It is not possible to pick Black chip from Box1. It is impossible event.

So , probability that Box1 was picked, given that the chip is black is zero