
Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as number greater than  1.

To find the probability distribution of the number of successes in two tosses of a die, where a success is defined as rolling a number greater than 1, we can follow these steps:

1. **Define the success probability for one toss:**
   - The die has 6 faces (1, 2, 3, 4, 5, 6).
   - Success is rolling a 2, 3, 4, 5, or 6, which gives 5 favorable outcomes.
   - The probability of success (\( p \)) is \( \frac{5}{6} \).
   - The probability of failure (\( q \)) is \( 1 - p = \frac{1}{6} \).

2. **Set up the distribution for two tosses:**
   - We are looking for the number of successes (\( X \)) in two tosses. \( X \) can take values 0, 1, or 2.

3. **Calculate the probabilities:**
   - \( P(X = 0) \): Probability of 0 successes (both tosses are failures)
     \[
     P(X = 0) = q \times q = \left(\frac{1}{6}\right) \times \left(\frac

Explore the probability distribution of successes in two tosses of a die, where success is defined as rolling a number greater than 1. Learn how to calculate probabilities for 0, 1, or 2 successes using basic probability theory. Suitable for Grades 10-12.

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