Question

Three coins are tossed, then
Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Probability of occurrence of 3 heads or 3 tails	I.	\(\frac{1}{8}\)
B.	Probability of occurrence of at least two heads	II.	\(\frac{7}{8}\)
C.	Probability of occurrence of at most two heads	III.	\(\frac{1}{2}\)
D.	Probability of occurrence of no head	IV.	\(\frac{1}{4}\)

Choose the correct answer from the options given below:

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

Hint:

List the 8 outcomes of three tosses and count favourable ones for each case.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Three coins give \(2^{3}=8\) equally likely outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. We find each probability and match it with List-II.

Step 2: Key Formula or Approach:
\(P(E)=\frac{\text{favourable outcomes}}{8}\). Count the favourable outcomes for each case.

Step 3: Case A.
3 heads or 3 tails: outcomes HHH and TTT, which is 2. So \(P=\frac{2}{8}=\frac{1}{4}\). This is IV.

Step 4: Case B.
At least two heads means 2 or 3 heads: HHT, HTH, THH, HHH, which is 4. So \(P=\frac{4}{8}=\frac{1}{2}\). This is III.

Step 5: Case C.
At most two heads means every outcome except HHH. That is 7 outcomes. So \(P=\frac{7}{8}\). This is II.

Step 6: Case D.
No head means TTT only, which is 1 outcome. So \(P=\frac{1}{8}\). This is I.

Step 7: Check the options.
The matching is A-IV, B-III, C-II, D-I. Option 1 pairs A with I, which is wrong. Option 2 pairs C with I, which is wrong. Option 3 pairs A with III, which is wrong. Option 4 is fully right.

Final Answer:
The correct matching is A-IV, B-III, C-II, D-I, option 4. \[ \boxed{\text{A-IV, B-III, C-II, D-I}} \]