Question

Four coins are tossed. What is the probability that two consecutive heads never occur together?

• A. $\dfrac{7}{8}$
• B. $\dfrac{1}{4}$
• C. $\dfrac{1}{3}$
• D. $\dfrac{1}{2}$

Hint:

In probability questions involving restrictions, always list valid outcomes carefully instead of subtracting blindly. This avoids counting errors.

Answer 1

The Correct Option is D

Step 1: Find the total number of possible outcomes.
Each coin has two possible outcomes: Head (H) or Tail (T).
Since four coins are tossed, total possible outcomes are:
\[ 2^4 = 16 \]
Step 2: List all outcomes where two heads do NOT occur together.
We must exclude all outcomes containing consecutive heads (HH).
Let us list all valid outcomes carefully.
Valid outcomes without consecutive heads are:
TTTT
TTTH
TTHT
THTT
HTTT
THTH
HTHT
HTTH
Step 3: Count the favorable outcomes.
The total number of favorable outcomes is 8.
Step 4: Compute the probability.
\[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} \]
\[ = \frac{8}{16} \]
\[ = \frac{1}{2} \]
Step 5: Final conclusion.
Hence, the probability that two consecutive heads never occur together is $\dfrac{1{2}$}.