A bag contains 5 red, 4 white and 3 blue beads. Three beads are selected at random without replacement. Find the probability that

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A bag contains 5 red, 4 white and 3 blue beads. Three beads are selected at random without replacement. Find the probability that

2. The beads selected were, white and blue:
• In that order
• In any order
3. No red bead is picked
4. Beads picked are of the same colour.

P(WWR or WBR or BBR or BWR)
(4/12 X 3/11 X 5/10) + 4/12 X 3/11 X 5/10
+ (3/12 x 2/11 x 5/10 + (3/12 x 4/11 x 5/10))
= 2/11
2. The beads selected were, white and blue: (2mks)
• In that order
5/12 x 4/11 x 3/10 = 1/22
• In any order
P(RWB or RBW or WBR or WRB or BWR or BRW)
(5/12 x 4/11 x 3/10) + (5/12 x 3/11 X 4/10)
+ (4/12 x 3/11 x 5/10)
6/52 = 3/11
3. No red bead is picked
P(BBB or BBW or BWB or BWW or WWW or WWB or WBW OR WBB)
(3/12 x 2/11 x 1/10)+(3/12x2/11x4/10)+(3/12x4/11x2/10)+(3/12x4/11x3/10 )+
(4/12x3/11x2/10)+(4/12x3/11x3/10) +(4/12x3/11x2/10)
=7/44
4. Beads picked are of the same colour.
P(BBB or WWW or RRR)
(3/12x2/11x1/10)+(4/12x3/11x2/10)+(5/12 x 4/11x3/10)
1/220 + 1/55 + 1/55 = 9/220