Question

If eight coins are tossed simultaneously, then the probability of getting at least six heads is:

• A. \( \frac{37}{64} \)
• B. \( \frac{37}{512} \)
• C. \( \frac{37}{256} \)
• D. \( \frac{37}{128} \)

Hint:

For probability problems involving multiple events, break them down by calculating the number of favorable outcomes for each condition and then sum them up.

Answer 1

The Correct Option is C

When tossing 8 coins, the total number of outcomes is \( 2^8 = 256 \). To get at least 6 heads, we calculate the number of ways to get 6, 7, and 8 heads.
The number of ways to get exactly 6 heads is \( \binom{8}{6} = \frac{8 \times 7}{2 \times 1} = 28 \).
The number of ways to get exactly 7 heads is \( \binom{8}{7} = 8 \).
The number of ways to get exactly 8 heads is \( \binom{8}{8} = 1 \).
Thus, the total number of favorable outcomes is \( 28 + 8 + 1 = 37 \).
Therefore, the probability is \( \frac{37}{256} \).