A weighted coin has a  
0.596
  probability of landing on heads. If you toss the coin  
12
  times, what is the probability of getting heads more than  
7
  times? (Round your answer to  
3
  decimal places if necessary.)

This is a binomial probability problem, where we are tossing a weighted coin 12 times, and the probability of getting heads is 0.596. We are asked to find the probability of getting heads more than 7 times, i.e., for the number of heads \( k > 7 \).

The binomial probability formula is:

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

Where:
- \( n \) is the number of trials (12 tosses),
- \( p \) is the probability of success (0.596),
- \( X \) is the random variable representing the number of heads,
- \( k \) is the number of heads (we want more than 7 heads).

To find the probability of getting more than 7 heads, we need to calculate:

\[
P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)
\]

I'll calculate this for you using binomial probability values for each of these outcomes.The probability of getting more than 7 heads in 12 tosses of a weighted coin with a probability of 0.596 of landing on heads is approximately \( 0.427 \) (rounded to 3 decimal places).

Would you like more details on the steps or any clarifications?

Here are some related questions:
1. How would the probability change if the number of tosses increases?
2. What is the probability of getting exactly 7 heads?
3. How does the probability of tails affect the outcome?
4. How would the distribution look graphically?
5. What happens if the coin is fair, i.e., with \( p = 0.5 \)?

**Tip**: The binomial distribution becomes more symmetric and approaches a normal distribution as the number of trials increases.

A weighted coin has a 0.596 probability of landing on heads. If you toss the coin 12 times, what is the probability of getting heads more than 7 times? (Round your answer to 3 decimal places if necessary.)

Learn how to calculate the probability of getting more than 7 heads in 12 tosses of a weighted coin with a 0.596 probability of landing heads. This problem covers key concepts in binomial probability and random variables. Suitable for students in Grades 10-12.

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