Math Problem Statement

You roll a die, pick a card, and spin the spinner. How many outcomes are possible?

Solution

To determine how many outcomes are possible when you roll a die, pick a card, and spin the spinner, we need to multiply the number of possible outcomes for each event:

  1. Rolling a die: There are 6 possible outcomes (the numbers 1 to 6).
  2. Picking a card: There are 6 possible outcomes (since there are 6 cards labeled from 1 to 6).
  3. Spinning the spinner: The spinner is divided into 4 sections, labeled "N," "K," "M," and "L." Thus, there are 4 possible outcomes.

Now, to find the total number of possible outcomes, we multiply the number of outcomes for each event: 6×6×4=1446 \times 6 \times 4 = 144

Thus, there are 144 possible outcomes.

Would you like further details or have any other questions?

Here are 5 related questions to expand on this concept:

  1. What if the die had 8 sides? How many outcomes would be possible?
  2. What is the probability of rolling a 4, picking the card labeled "3," and landing on "M"?
  3. If you removed one card, how would that affect the total number of outcomes?
  4. How does the concept of independent events apply in this scenario?
  5. How could you calculate the probability of landing on a specific card, number, and letter combination?

Tip: When calculating outcomes for independent events, always multiply the number of possibilities for each event!

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Math Problem Analysis

Mathematical Concepts

Probability
Multiplication Principle of Counting

Formulas

Total outcomes = number of outcomes (die) × number of outcomes (card) × number of outcomes (spinner)

Theorems

Multiplication Principle of Counting

Suitable Grade Level

Grades 4-6