# Math(more about probability)

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.

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.

### 1 Answer

- ten13kidneyLv 51 decade agoFavorite Answer
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.