QuestionIn a standard deck of cards, what is the probability that you will get a 2 or a face card? Provide four decimal digits.
Add your answer Integer, decimal, or E notation allowed $\qquad$ 2 Poin
Question 7
Two fair dice are thrown. What is the probability that the sum shown on the dice is divisible by 5? Provide four decimal digits.
Add your answer Integer, decimal, or Enotation allowed

STEP 1

1. A standard deck of cards has 52 cards.
2. A face card is a Jack, Queen, or King.
3. There are 4 suits: hearts, diamonds, clubs, and spades.
4. Each suit contains one 2 and three face cards (Jack, Queen, King).
5. Two fair six-sided dice are used.
_HIGH_LEVEL_APPROACH_ for the first problem:
1. Calculate the total number of favorable outcomes for drawing a 2 or a face card.
2. Calculate the probability of drawing a 2 or a face card.
_HIGH_LEVEL_APPROACH_ for the second problem:
1. Determine the total number of possible outcomes when two dice are thrown.
2. Identify the outcomes where the sum is divisible by 5.
3. Calculate the probability of the sum being divisible by 5.
**First Problem: Probability of drawing a 2 or a face card**

STEP 2

STEP 3

Calculate the number of 2s in the deck:
There are 4 suits, and each suit has one 2.
$$\text{Number of 2s} = 4$$

STEP 4

Calculate the number of face cards in the deck:
Each suit has 3 face cards (Jack, Queen, King), so:
$$\text{Number of face cards} = 4 \times 3 = 12$$

STEP 5

Calculate the total number of favorable outcomes:
$$\text{Total favorable outcomes} = 4 + 12 = 16$$

STEP 6

Calculate the probability of drawing a 2 or a face card:
$$\text{Probability} = \frac{16}{52} = \frac{4}{13} \approx 0.3077$$
**Second Problem: Probability of the sum being divisible by 5**
STEP_1: Calculate the total number of possible outcomes when two dice are thrown:
Each die has 6 faces, so:
$$\text{Total outcomes} = 6 \times 6 = 36$$
STEP_2: Identify the outcomes where the sum is divisible by 5:
Possible sums divisible by 5 are 5 and 10.
- Sum of 5: (1,4), (2,3), (3,2), (4,1) - Sum of 10: (4,6), (5,5), (6,4)
Total favorable outcomes:
$$4 + 3 = 7$$
STEP_3: Calculate the probability of the sum being divisible by 5:
$$\text{Probability} = \frac{7}{36} \approx 0.1944$$
The probability for the first problem is:
$$\boxed{0.3077}$$
The probability for the second problem is:
$$\boxed{0.1944}$$