Question

A glass jar contains 1 red, 3 green, 2 blue and 4 yellow marbles. If a single marble is chosen at random from the jar
(A)Probability of getting a yellow marble is \(\frac{1}{5}\)
(B) Probability of getting a green marble is \(\frac{3}{10}\)
(C) Probability of getting either a yellow or a green marble is \(\frac{7}{10}\)
(D) Probability of getting either a red or a yellow marble is \(\frac{3}{10}\)
Choose the correct answer from the options given below:

• (A) and (D) only
• (B) and (C) only
• (A) and (C) only
• (B) and (D) only

Answer 1

The Correct Option is B

To solve the problem of determining the correct probabilities, we need to first understand the given counts of different colored marbles in the jar and use the basic formula of probability. The total number of marbles is the sum of all colored marbles.

Let's calculate step-by-step:

1. Total number of marbles in the jar: 

\(1\ (\text{red}) + 3\ (\text{green}) + 2\ (\text{blue}) + 4\ (\text{yellow}) = 10\)

1. Probability of getting a yellow marble:

\(P(\text{Yellow}) = \frac{\text{Number of yellow marbles}}{\text{Total marbles}} = \frac{4}{10} = \frac{2}{5}\)

1. This contradicts option (A) which states \(\frac{1}{5}\).
2. Probability of getting a green marble:

\(P(\text{Green}) = \frac{3}{10}\)

1. This matches with option (B).
2. Probability of getting either a yellow or a green marble:

\(P(\text{Yellow or Green}) = P(\text{Yellow}) + P(\text{Green}) = \frac{2}{5} + \frac{3}{10} = \frac{4}{10} + \frac{3}{10} = \frac{7}{10}\)

1. This matches with option (C).
2. Probability of getting either a red or a yellow marble:

\(P(\text{Red or Yellow}) = P(\text{Red}) + P(\text{Yellow}) = \frac{1}{10} + \frac{2}{5} = \frac{1}{10} + \frac{4}{10} = \frac{5}{10} = \frac{1}{2}\)

1. This does not match with option (D) which claims \(\frac{3}{10}\).

From the above calculations, the correct statements are: (B) the probability of getting a green marble is \(\frac{3}{10}\) and (C) the probability of getting either a yellow or a green marble is \(\frac{7}{10}\).

Therefore, the correct answer is (B) and (C) only.