Math Problem Statement

A quarter and a nickel are tossed. How many outcomes are possible?

Solution

When a quarter and a nickel are tossed, each coin has 2 possible outcomes: Heads (H) or Tails (T).

The total number of outcomes can be calculated by multiplying the outcomes of each coin: 2×2=42 \times 2 = 4

The possible outcomes are:

  1. Quarter - Heads, Nickel - Heads (HH)
  2. Quarter - Heads, Nickel - Tails (HT)
  3. Quarter - Tails, Nickel - Heads (TH)
  4. Quarter - Tails, Nickel - Tails (TT)

So, the correct answer is 4.

Would you like more details or have any other questions?

Here are some related questions:

  1. What if three coins are tossed instead of two?
  2. How would the answer change if one of the coins were a die instead?
  3. What is the probability of getting at least one head in this case?
  4. How many outcomes are possible with three different coins?
  5. How many outcomes are possible if the coins are biased?

Tip: The total number of outcomes when tossing multiple independent coins is calculated by raising 2 to the power of the number of coins.

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Math Problem Analysis

Mathematical Concepts

Probability
Combinatorics

Formulas

Total outcomes = 2^n, where n is the number of coins

Theorems

Fundamental principle of counting

Suitable Grade Level

Grades 6-8