Consider a deck of 52 cards with the following characteristics:
13 red cards, numbered 1 through 13
13 blue cards, numbered 1 through 13
13 green cards, numbered 1 through 13
13 black cards, numbered 1 through 13
1. Describe the steps necessary to calculate the theoretical probability of:
a. Drawing two red cards one after the other from the given deck if the cards are returned to the deck after each pick.
b. Drawing three cards with the same value one after the other from the given deck without replacing them in the deck after each pick.
2. Describe the steps necessary to calculate the experimental probabilities of:
a. Drawing two red cards one after the other from the given deck if the cards are returned to the deck after each pick.
b. Drawing three cards with the same value one after the other from the given deck without replacing them in the deck after each pick.
I will be happy to critique your thinking on this.
To calculate the theoretical probability, follow these steps:
1. Determine the total number of possible outcomes.
- In this case, the total number of cards is 52.
2. Determine the favorable outcomes for the desired event.
a. Drawing two red cards one after the other (with replacement):
- Since the cards are returned to the deck after each pick, the total number of red cards available for the first draw is 13, and the same for the second draw. So, the favorable outcomes are (13/52) * (13/52) = 169/2704.
b. Drawing three cards with the same value one after the other (without replacement):
- For the first card, any card can be chosen out of 52.
- For the second card, there are only three cards with the same value, and the deck now has 51 cards remaining.
- For the third card, there are only two cards with the same value left, and the deck now has 50 cards remaining.
- So, the favorable outcomes are (52/52) * (3/51) * (2/50) = 6/850.
To calculate the experimental probabilities, follow these steps:
1. Perform a series of repeated experiments or trials where the event is observed.
2. Count the number of times the desired event occurs during the trials.
3. Divide the number of times the event occurs by the total number of trials to get the experimental probability.
a. Drawing two red cards one after the other (with replacement):
- Start drawing two cards repeatedly, note down the number of times two red cards are drawn one after the other.
- Repeat the experiment a large number of times (e.g., 1000) to get reliable results.
- The experimental probability is the number of times two red cards are drawn one after the other divided by the total number of trials.
b. Drawing three cards with the same value one after the other (without replacement):
- Start drawing three cards repeatedly, note down the number of times three cards with the same value are drawn one after the other.
- Repeat the experiment a large number of times (e.g., 1000) to get reliable results.
- The experimental probability is the number of times three cards with the same value are drawn one after the other divided by the total number of trials.
Note: The experimental probability might differ slightly from the theoretical probability due to random variations in the experimental results. The larger the number of trials, the closer the experimental probability will be to the theoretical probability.