A weighted coin has a 0.472 probability of landing on heads. If you toss the coin 16 times, what is the probability of getting heads no more than 5 times?

Round your answer to three decimal places. 

This problem involves a **binomial distribution**, as you're dealing with repeated independent trials (coin tosses) with two possible outcomes (heads or tails). The formula for the binomial probability is:

\[
P(X = k) = \binom{n}{k} p^k (1 - p)^{n-k}
\]

Where:
- \( n \) = number of trials (in this case, 16 tosses),
- \( k \) = number of successes (number of heads),
- \( p \) = probability of success (probability of heads, 0.472),
- \( 1 - p \) = probability of failure (probability of tails).

You want the probability of getting **no more than 5 heads** (i.e., \( P(X \leq 5) \)), which means you need to sum the probabilities for 0, 1, 2, 3, 4, and 5 heads.

Let me calculate this for you.The probability of getting heads no more than 5 times in 16 tosses of the coin is approximately **0.152** (rounded to three decimal places).

Do you want more details or have any questions?

Here are some related questions:
1. What is the probability of getting exactly 5 heads in 16 tosses?
2. How would the result change if the probability of heads were 0.6 instead of 0.472?
3. What is the expected number of heads in 16 tosses with a 0.472 probability of heads?
4. How do you calculate the standard deviation for the number of heads in this scenario?
5. What is the probability of getting more than 10 heads in 16 tosses?

**Tip:** The binomial distribution is useful for situations where you repeat the same experiment with two outcomes, like flipping a weighted coin multiple times.

A weighted coin has a 0.472 probability of landing on heads. If you toss the coin 16 times, what is the probability of getting heads no more than 5 times?

Calculate the probability of getting no more than 5 heads in 16 tosses of a weighted coin with a 0.472 probability of heads. This problem involves key concepts from probability theory and binomial distribution. Suitable for students in Grades 10-12.

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