Two cards are drawn in succession from a deck without replacement. What is the probability that both cards are greater than 2 and less than 8?
Well, the probability of drawing a card greater than 2 and less than 8 from a standard deck is like trying to find a unicorn at a zoo.
But since I'm feeling generous, let me calculate it for you.
First, let's find the number of cards that fit the criteria. Between 2 and 8, we have 5 cards: 3, 4, 5, 6, and 7. There are 4 of each suit, so that's a total of 20 cards.
Now, let's calculate the total number of possible outcomes. In a standard deck, there are 52 cards. When you draw the first card, you have 52 options. After that, there are only 51 cards left to choose from.
So, the probability of drawing a card greater than 2 and less than 8 on the first draw is 20/52. And on the second draw, since we're drawing without replacement, there will be 19 cards left in the deck, and 19/51 of those will fit the criteria.
To find the probability of both events occurring, we multiply the probabilities together:
(20/52) * (19/51) ≈ 0.134
So, the probability of drawing two cards greater than 2 and less than 8 is approximately 0.134, or about a 13.4% chance. Good luck finding those elusive unicorns!
To calculate the probability that both cards are greater than 2 and less than 8, we need to determine the total number of favorable outcomes and the total number of possible outcomes.
There are four cards greater than 2 and less than 8 in each suit (3, 4, 5, 6). Since there are 4 suits in a deck (clubs, diamonds, hearts, spades), the total number of favorable outcomes is 4 * 4 = 16.
When drawing the first card, there are 52 possible cards to choose from. However, once the first card is drawn, there are only 51 cards remaining in the deck for the second draw. Thus, the total number of possible outcomes is 52 * 51 = 2652.
Therefore, the probability of drawing two cards greater than 2 and less than 8 is 16 / 2652, which simplifies to 4 / 663 or approximately 0.0060 (rounded to 4 decimal places).
To find the probability that both cards are greater than 2 and less than 8, we need to first determine the total number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the total number of possible outcomes:
In a standard deck of 52 playing cards, there are no restrictions on the first card drawn. Therefore, there are 52 possible choices for the first card.
After drawing the first card, there are now 51 cards remaining in the deck, which reduces the number of choices for the second card. Hence, for the second card, there are 51 possible choices.
Therefore, the total number of possible outcomes is 52 * 51 = 2,652.
Step 2: Determine the total number of favorable outcomes:
To find the number of cards that are greater than 2 and less than 8, we need to count the number of cards that satisfy this condition.
There are 3 cards greater than 2 in each suit: 3, 4, 5, 6, 7. Since there are 4 suits in a deck, the total number of cards greater than 2 and less than 8 is 3 * 4 = 12.
After drawing the first card, there will be 11 cards remaining that satisfy the condition for the second card.
Therefore, the total number of favorable outcomes is 12 * 11 = 132.
Step 3: Calculate the probability:
The probability of an event is defined as the ratio of the number of favorable outcomes to the number of possible outcomes.
P(both cards are greater than 2 and less than 8) = Number of favorable outcomes / Number of possible outcomes
= 132 / 2652
= 0.0498 (approximately)
So, the probability that both cards drawn are greater than 2 and less than 8 is approximately 0.0498, or roughly 4.98%.
3-7 = 5 possibilities * 4 suits = 20
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
20/52 * (20-1)/(52-1) = ?