Jorge has a standard deck of cards and a six-sided number cube. What is the probability that he will draw a diamond from the deck of cards and roll a number greater than two?
To find the probability that Jorge will draw a diamond from the deck of cards and roll a number greater than two, we need to determine three things:
1. The number of favorable outcomes: the number of cards that are diamonds and the number of outcomes on the number cube that are greater than two.
2. The total number of possible outcomes: the total number of cards in the deck and the total number of possible outcomes on the number cube.
3. Calculate the probability: Divide the number of favorable outcomes by the total number of possible outcomes.
Let's break it down step by step.
1. The number of favorable outcomes:
- In a standard deck of cards, there are 52 cards, and 13 of those cards are diamonds.
- On a six-sided number cube, there are six possible outcomes (numbers 1 through 6). We need to determine how many of those outcomes are greater than two, which are numbers 3, 4, 5, and 6.
So, the number of favorable outcomes is 13 (diamond cards) multiplied by 4 (numbers greater than two on the number cube) which equals 52.
2. The total number of possible outcomes:
- The total number of cards in a standard deck is 52.
- The total number of possible outcomes on a six-sided number cube is 6.
So, the total number of possible outcomes is 52 (number of cards) multiplied by 6 (number of possibilities on the number cube), which equals 312.
3. Calculate the probability:
Divide the number of favorable outcomes (52) by the total number of possible outcomes (312).
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 52 / 312
Probability = 0.1667 (rounded to four decimal places) or approximately 16.67%
Therefore, the probability that Jorge will draw a diamond from the deck of cards and roll a number greater than two is approximately 16.67%.