Question

five marbles are placed in a jar. two marbles are red, and the rest are blue. suppose you select 3 random marbles from the jar without looking. you do not replace the marbles what is the probability that at least one of the marbles is blue. write the answer as a decimal

Answer 1

Let B represent blue marble and

R represent red marble

At least one of the marble is blue means the combination becomes

BBR or BRB or RBB or RRB or RBR or BRR or BBB

Where the three letters in each case means the first is picked, then the second and then the third.

Now we have 3 possiblities of picking 2 blue marbles and 1 red marble (BBR or BRB or RBB) and

3 possibilities of picking 2 red marbles and 1 blue marble (RRB or RBR or BRR)

and finally one possibility of picking all blue marbles (BBB)

Hence the probability of picking 2 blue marbles and 1 red marble is

`\begin{gathered} 3((3)/(5)*(2)/(4)*(2)/(3)_{}) \\ =0.6 \end{gathered}`

The probability of picking 2 red marbles and 1 blue marble is

`\begin{gathered} 3((2)/(5)*(1)/(4)*(3)/(3)_{}) \\ 0.3 \end{gathered}`

The probability of all blue marbles becomes

`\begin{gathered} (3)/(5)*(2)/(4)*(1)/(3) \\ 0.1 \end{gathered}`

Hence the required probability is 0.6 + 0.3 + 0.1 = 1.0

Hence the answer is 1.0

Also another way is, since there are 3 blue marbles and you are picking 3 marbles at a time, you must pick at least one blue marble, because there are only 2 red marbles, hence, the third mable must be blue. So the probability is 1 or you can say 1.0 as a decimal