Math Problem Statement
coin is tossed 9 times.
What is the probability of getting all tails? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
Solution
Each toss of a fair coin has two possible outcomes: heads (H) or tails (T). Since the coin is tossed 9 times, the probability of getting tails in each individual toss is .
To calculate the probability of getting all tails in 9 tosses, we raise the probability of getting tails in one toss to the power of 9:
Thus, the probability of getting all tails when a coin is tossed 9 times is:
As a decimal, this is:
So, the probability is approximately 0.001953, or exactly .
Would you like more details on how this probability is derived?
Here are 5 related questions:
- What is the probability of getting at least one head in 9 tosses?
- What is the probability of getting exactly 5 tails in 9 tosses?
- If a coin is tossed 10 times, what is the probability of getting all heads?
- How would the probability change if the coin were biased with a 0.6 chance of tails?
- What is the expected number of tails when tossing a coin 9 times?
Tip: The probability of independent events happening consecutively is the product of their individual probabilities.
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Math Problem Analysis
Mathematical Concepts
Probability
Independent Events
Formulas
P(all tails) = (1/2)^n, where n is the number of tosses
Theorems
Probability of Independent Events
Suitable Grade Level
Grades 6-8