A box contains 5 blue beads, 4 yellow beads and 3 purple beads.
Three beads are taken from the bag, at random, without replacement.
a) What is probability of picking, in order, a blue bead followed
by a yellow bead followed by a purple bead?
b) Work out the probability that all three beads will be the same colour.
c) What is the probability that the three beads will not be the same colour?
Please work out only these!
Answers
Answer:
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.