Question

What is the probability of getting three heads if seven coins are tossed together?

• A. $\dfrac{35}{128}$
• B. $\dfrac{21}{128}$
• C. $\dfrac{7}{128}$
• D. $\dfrac{1}{8}$

Hint:

For coin toss problems, always use combinations to count favorable outcomes.

Answer 1

The Correct Option is A

Step 1: Total possible outcomes.
When 7 coins are tossed, the total number of possible outcomes is:
\[ 2^7 = 128 \]
Step 2: Favorable outcomes.
The number of ways of getting exactly 3 heads out of 7 coins is given by:
\[ \binom{7}{3} = 35 \]
Step 3: Calculating probability.
Probability = $\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$
\[ = \dfrac{35}{128} \]
Step 4: Conclusion.
The required probability is $\dfrac{35}{128}$.