Question

A Glass Jar contains 1 Red, 3 Green, 2 Blue and 4 Yellow marbles. If a single marble is chosen then Match List I with List II:

List I	List II
(A) Probability of yellow marble	(I) \(\frac{1}{3}\)
(B) Probability of green marble	(II)\(\frac{7}{10}\)
(C) Probability of either green or yellow marble	(III) \(\frac{1}{2}\)
(D) Probability of either red or yellow marble	(IV) \(\frac{4}{10}\)

Choose the correct answer from the options given below

• A. (A)-(II), (B)-(III), (C)-(IV), (D)-(1)
• B. (A)-(1), (B)-(IV), (C)-(II), (D)-(III)
• C. (A) - (IV) B)-(I), (C)-(II), (D)-(III)
• D. (A)-(IV), (B)-(II), (C)-(III), (D)-(1)

Answer 1

The Correct Option is C

To solve this problem, we need to calculate the probability of drawing different colored marbles and then match them to the probabilities given in List II.

1. Calculate Total Number of Marbles:
   • Red Marbles = 1
   • Green Marbles = 3
   • Blue Marbles = 2
   • Yellow Marbles = 4
2. Probability of Drawing a Yellow Marble (List I A):
   • The number of yellow marbles = 4
   • Probability of yellow marble = \(\frac{4}{10} = \frac{2}{5}\)
3. Probability of Drawing a Green Marble (List I B):
   • The number of green marbles = 3
   • Probability of green marble = \(\frac{3}{10}\)
4. Probability of Either Green or Yellow Marble (List I C):
   • The number of green or yellow marbles = 3 + 4 = 7
   • Probability of green or yellow marble = \(\frac{7}{10}\)
5. Probability of Either Red or Yellow Marble (List I D):
   • The number of red or yellow marbles = 1 + 4 = 5
   • Probability of red or yellow marble = \(\frac{5}{10} = \frac{1}{2}\)

Now, let's match these probabilities with List II:

• (A) Probability of yellow marble = \(\frac{2}{5} = \frac{4}{10}\) which matches the given choice in List II: (IV) \(\frac{4}{10}\)
• (B) Probability of green marble = \(\frac{3}{10}\) which matches the given choice (I) \(\frac{1}{3}\). However, this seems uncommon here as \(\frac{3}{10}\) is closest.
• (C) Probability of either green or yellow marble = (II) \(\frac{7}{10}\)
• (D) Probability of either red or yellow marble = (III) \(\frac{1}{2}\)

By matching these probabilities, we conclude the correct answer:

(A) - (IV), (B) - (I), (C) - (II), (D) - (III).

Answer 2

Total number of marbles = \( 1 + 3 + 2 + 4 = 10 \). Probability of choosing a yellow marble: \[ P(\text{Yellow}) = \frac{4}{10} = 0.4 = (\text{IV}) \] Probability of choosing a green marble: \[ P(\text{Green}) = \frac{3}{10} = 0.3 = (\text{I}) \] Probability of choosing either a green or yellow marble: \[ P(\text{Green or Yellow}) = \frac{3 + 4}{10} = \frac{7}{10} = 0.7 = (\text{II}) \] Probability of choosing either a red or yellow marble: \[ P(\text{Red or Yellow}) = \frac{1 + 4}{10} = \frac{5}{10} = 0.5 = (\text{III}) \] Thus, the correct matches are: (C)-(IV), (B)-(I), (C)-(II), (D)-(III).