f.3 probability

Total numbers of balls = 3+4+5 = 12

a) P(both red)
=(3/12)(2/11)
= 1/22

b) P(different colours)
=1-P(same colour)
=1-P(both red)-P(both white)-P(both black)
=1-1/22-(4/12)(3/11)-(5/12)(4/11)
=1-1/22-1/11-5/33
=47/66

c) Expected number of coupons rewarded
=20(1/22)+10(47/66)
= 8 {8.0303}

Total number of balls=3+4+5=12
a)
probability that the balls drawn are both red
=P( 1st ball drawn is red) * P( 2nd ball drawn is red)
= 3/12 *2/11
=1/22

b)probability that the balls are of different colours
=probability that two balls are NOT same colours

probability that the balls drawn are both white
=P( 1st ball drawn is white) * P( 2nd ball drawn is white)
= 4/12 *3/11
=1/11

probability that the balls drawn are both black
=P( 1st ball drawn is black) * P( 2nd ball drawn is black)
= 5/12 *4/11
=5/33

probability that two balls are same colours
=probability that the balls drawn are both red
+probability that the balls drawn are both white
+probability that the balls drawn are both black
=1/22+1/11+5/33
=19/66

probability that the balls are of different colours
=probability that two balls are NOT same colours
=1-probability that two balls are same colours
=1-19/66
=47/66

c)
expect number of coupons rewarded
=probability that the balls are of different colours *number of cupons get when the balls are of different colours
+probability that the balls are both red*number of cupons get when the both balls are red
=47/66*10+1/22*20
=265/33

(a) P(the probability that the balls drawn are both red)
=(3/12)(2/11)
=1/22

(b) P(the probability that the balls are of different colours)
=1-P(two red balls)-P(two white balls)-P(two black balls)
=47/66

(c) The expect number of coupons rewarded
=20(1/22)+10(47/66)
~8 coupons