A box contains 5 blue beads, 4 yellow beads and 3 purple bead. Three beads are taken from the bag, at random, without replacement.[Is is a box or a bag? Hahahaha!]
a) What is the probability of picking, in order, a blue bead followed by a yellow bead followed by a purple bead?
There are 5+4+3=12 beads.
To succeed in picking the first bead blue,
we can choose the first bead as any of the 5 blue beads out of the 12
beads.
That's a probability of 5/12 of picking the first bead.
Since we are not replacing the beads, there will only be 11 beads remaining.
To succeed once we've succeed in picking the first bead blue,
we can choose the second bead as any of 4 yellow beads out of the remaining
11 beads.
That's a probability of 4/11 of picking the second bead successfully once
we've picked the first bead successfully.
Since we are not replacing the beads, there are only 10 beads left.
To succeed once we've succeed in picking the first bead blue and the second
bead yellow, we can choose the third bead as any of 3 purple beads out of
the remaining 10 beads.
That's a probability of 3/10 of picking the third bead successfully once
we've picked the first and second beads successfully.
Answer:
b) Work out the probability that all three beads will be the same colour.
P(all blue)+P(all yellow)+P(all purple) =
c) What is the probability that the three beads will not be the same color?[Do you mean "not all the same color, or "all three different colors?"]
If you mean "not all the same color" then it is the complement event of (b)
Answer =
If you mean "all three different colors", then it's just a matter of
multiplying the results of the part a) by 3! or 6 because it's just as
likely that they are all different in one order and another.
Answer:
Edwin