Question

Each of the marbles in a jar is either red or white or blue. If one marble is to be selected at random from the jar, what is the probability that marble will be blue?
(1) There are a total of 24 marbles in the jar, 8 of which are red.
(2) The probability that marble selected will be white is $\dfrac{1}{2}$.
The mark the correct option:
(a) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(b) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(c) Both statements together are sufficient, but neither statement alone is sufficient.
(d) Each statement alone is sufficient.
(e) Both statements together are not sufficient

Answer 1

Hint: Three marbles of color, red, white or blue given and one of the marble is drawn at random. Now, we have to comment upon the two statements given in the above problem. Let us consider that statement (1) is true then through statement (1) we know the total marbles in the jar and number of red marbles also. Now, let us assume that statement (2) is also true which says that the probability of marble is $\dfrac{1}{2}$ then see if using both the statements we are getting the probability of blue marbles or either statement (1) or (2) are giving.

Complete step-by-step answer:
We have given a jar which contains either red, blue and white marbles and we have drawn a marble at random. We have to find the probability when the marble drawn is blue.
Using the information of Statement (1) which says that there are 24 marbles in the jar and number of red marbles are 8.
The Statement (2) says that the probability that the marble drawn in white is $\dfrac{1}{2}$. Let us assume that statement (1) is true statement (2) is also true then multiplying the probability of drawing a white marble to the total number of marbles which are 24 we get the number of white marbles.
$\begin{align}
  & \dfrac{1}{2}\left( 24 \right) \\
 & =12 \\
\end{align}$
Hence, we got the number of white marbles as 12.
Now, we know the number of white marbles as 12, and the number of red marbles as 8. We can find the number of blue marbles by subtracting the addition of the red and white marbles from the total marbles.
$\begin{align}
  & 24-\left( 12+8 \right) \\
 & =24-20 \\
 & =4 \\
\end{align}$
From the above, we got the number of blue marbles as 4. Now, to find the probability of selecting a blue marble from the jar we are going to divide the number of blue marbles (4) by total marbles (24).
$\begin{align}
  & \dfrac{4}{24} \\
 & =\dfrac{1}{6} \\
\end{align}$
As you can see that by using both the statements (1 & 2) and neither of the two statements alone are sufficient we are getting the probability of drawing a blue marble so the correct option is (c).

So, the correct answer is “Option c”.

Note: The important thing to be noted in this problem is that the same color marbles given are identical. You can distinguish the different color marbles but you cannot distinguish the same color marbles that’s why we have written the probability of selecting a blue marble by keeping into consideration that same color marbles are alike.