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 12\frac{1}{2}.

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:

P(all tails)=(12)9=1512P(\text{all tails}) = \left( \frac{1}{2} \right)^9 = \frac{1}{512}

Thus, the probability of getting all tails when a coin is tossed 9 times is:

1512\frac{1}{512}

As a decimal, this is:

15120.001953\frac{1}{512} \approx 0.001953

So, the probability is approximately 0.001953, or exactly 1512\frac{1}{512}.

Would you like more details on how this probability is derived?

Here are 5 related questions:

  1. What is the probability of getting at least one head in 9 tosses?
  2. What is the probability of getting exactly 5 tails in 9 tosses?
  3. If a coin is tossed 10 times, what is the probability of getting all heads?
  4. How would the probability change if the coin were biased with a 0.6 chance of tails?
  5. 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