A six-sided number cube is rolled and a card is drawn from a standard deck of 52 cards. Find the total number of outcomes.
What is the probability of rolling a number greater than 4 and drawing a king from the deck?
any card with any cube face ... 52 * 6
>4 means 5 or 6 ... 1/3 of the faces
... 4 kings in 52 cards
... 1/3 * 1/13
PLEASE HELP AS SOON AS POSSIBLE
On six-sided number cube the numbers greater than 4 are:
5 and 6
There are two numbers greater than 4.
The probability these numbers will be rolling is:
2 / 6 = 1 / 3
Standard deck of 52 cards have 4 kings.
The probability that the king will be pulled out is 4 / 52 = 4 ∙ 1 / 4 ∙ 13 = 1 / 13
The probability of rolling a number greater than 4 and drawing a king from the deck is:
1 / 3 ∙ 1 / 13 = 1 / 39
To find the total number of outcomes, we need to multiply the number of outcomes for rolling the number cube by the number of outcomes for drawing a card from the deck.
1. Rolling the number cube: Since it is a standard six-sided cube, there are 6 possible outcomes (numbers 1 through 6).
2. Drawing a card from the deck: The standard deck of 52 cards includes 4 suits (hearts, diamonds, clubs, and spades) with 13 cards each. So, there are 52 possible outcomes.
To find the total number of outcomes, we multiply the number of outcomes for each event: 6 (number cube outcomes) × 52 (card outcomes) = 312.
The total number of outcomes is 312.
Next, let's calculate the probability of rolling a number greater than 4 and drawing a king from the deck.
1. Rolling a number greater than 4: Since there are two numbers greater than 4 on a six-sided cube (5 and 6), the probability of rolling a number greater than 4 is 2/6 or simplified to 1/3.
2. Drawing a king from the deck: There are 4 kings in a standard deck (one king in each suit). Therefore, the probability of drawing a king is 4/52, which can be simplified as 1/13.
To find the overall probability, we multiply the probabilities of each event: (1/3) × (1/13) = 1/39.
So, the probability of rolling a number greater than 4 and drawing a king from the deck is 1/39.