1.There are 1 red ball pen and 2 black ball pens in box A,and 2 red ball pens and 3green ball pens in box B.If a pen is drawn from each bax at random,find the probability that

(a)the two ball pens are same in colour.

(b)the two ball pens are in different colours.

Update:

2.There are pairs of pants in white,blue,black and purple each in drawer A.There are T-shirts in white,blue,black and purple each in drawer B.If a pair of plants and a T-shirt are taken from drawers A and B respectively at random,find the probability that they are in different colours.

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1. The probability of having the ball pen drawn from Box A is red = 1/3

The probability of having the ball pen drawn from Box A is balck= 2/3;

The probability of having the ball pen drawn from Box B is red = 2/5

The probability of having the ball pen drawn from Box B is green = 3/5.

(a) probability that the two ball pens are same in colour

= probability that both the two ball pens are red

= (probability that the ball pen drawn from Box A is red) x (probability that the ball pen drawn from Box B is red) [ since these two events are independent)

= (1/3)(2/5) = 2/15.

(b) similarly, probability that the two ball pens are in differnt colours

= [probability (red from Box A)][probability (green from Box B)] + [probability (black from Box A)][probability (red or green from Box B]

= (1/3)(3/5) + (2/3)(1)

= 1/5 + 2/3

= 13/15.

Alernatively, probability that the two ball pens are in different colours

= 1 - probability that the two ball pens are in same colour

= 1- 2/15 (see (a) above)

= 13/15.

2. There are 4 pairs of pants, each of different colour, in drawer A; and 4 T-shirts, again each of different colour, in drawer B.

Probability that the pants and T-shirt taken are in different colour

= [probability(white pants)][probability of (not white T-shirt] +

[probability(blue pants)][probability of (not blue T-shirt)]+

[probability (black pants)][probability(not black T-shirt)]+

[probability (purple pants)][probability(not purple T-shirt)]

= (1/4)(3/4) + (1/4)(3/4) + (1/4)(3/4) + (1/4)(3/4)

= 3/16 + 3/16+3/16+ 3/16

= 12/16= 3/4.

Alternatively, probability required = 1 - probability( pants and T-shirt are in same colour) = 1- 4(1/4)(1/4) = 3/4.