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. | \( \displaystyle\frac{1}{8} \) |
| B. | Probability of occurrence of at least two heads | II. | \( \displaystyle\frac{7}{8} \) |
| C. | Probability of occurrence of at most two heads | III. | \( \displaystyle\frac{1}{2} \) |
| D. | Probability of occurrence of no head | IV. | \( \displaystyle\frac{1}{4} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A-IV, B-III, C-II, D-I
Tossing three coins gives \( 2^3=8 \) equally likely outcomes:
HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
(A) Probability of occurrence of 3 heads or 3 tails
This matches (IV) 1/4. The favourable outcomes are HHH and TTT.
\( \displaystyle P=\frac{2}{8}=\frac{1}{4} \)
(B) Probability of occurrence of at least two heads
This matches (III) 1/2. The favourable outcomes are HHH, HHT, HTH and THH.
\( \displaystyle P=\frac{4}{8}=\frac{1}{2} \)
(C) Probability of occurrence of at most two heads
This matches (II) 7/8. Every outcome except HHH has at most two heads.
\( \displaystyle P=1-\frac{1}{8}=\frac{7}{8} \)
(D) Probability of occurrence of no head
This matches (I) 1/8. The only favourable outcome is TTT.
\( \displaystyle P=\frac{1}{8} \)
So the matching is A-IV, B-III, C-II, D-I.