Math Problem Statement

probiaiblty of getting escatly two tails

Solution

To find the probability of getting exactly two tails when flipping a coin multiple times, we need to know the total number of flips. Assuming you're referring to flipping a coin three times (a common scenario), here's how you'd calculate it:

  1. Identify the total possible outcomes:
    When flipping a coin three times, each flip has 2 possible outcomes (heads or tails). So, the total number of outcomes is 23=82^3 = 8.

  2. List the outcomes where there are exactly two tails:
    The outcomes with exactly two tails are: HTT, THT, and TTH. There are 3 such outcomes.

  3. Calculate the probability:
    The probability of getting exactly two tails is the number of favorable outcomes divided by the total number of outcomes:
    Probability=38=0.375\text{Probability} = \frac{3}{8} = 0.375

So, the probability of getting exactly two tails in three flips is 38\frac{3}{8} or 0.375.

Would you like to go into more detail on this, or do you have any questions?

Here are 5 related questions:

  1. What is the probability of getting exactly two heads in three flips?
  2. How does the probability change if you flip the coin four times?
  3. What is the probability of getting at least one tail in three flips?
  4. How many outcomes have no tails in three flips?
  5. What is the probability of getting exactly one tail in three flips?

Tip: When dealing with probabilities,

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Math Problem Analysis

Mathematical Concepts

Probability Theory
Combinatorics

Formulas

Probability calculation formula: P(E) = \frac{n(E)}{n(S)}

Theorems

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Suitable Grade Level

Grades 7-9