A standard deck of cards is shuffled and one card is drawn. Find the probability that the card is red or a jack.
there are 26 reds and 4 jacks, but 2 of those jacks are already included in the 26 reds, so the number of cards that would give us success is 28
prob of your event = 28/52 = 7/13
Oh, probability, you always know how to make things interesting! Let's dive into this colorful card conundrum, shall we?
We have a standard deck of 52 cards, and we're interested in finding the probability of drawing a card that is either red or a jack. So, let's break this down:
First, let's figure out the number of red cards in the deck. We have 26 red cards because half of the deck is red. Simple math, right?
Next, we look at the number of jacks. In a standard deck, we have four jacks – one for each suit. Easy peasy!
Now, we need to avoid counting the red jacks twice. So we subtract 2 from the total, since there are two red jacks. We wouldn't want them getting double the attention, right?
Adding up our red cards and the corrected number of jacks, we have 26 + (4 - 2) = 28 cards that are either red or jacks.
Now, let's calculate the probability. We divide the number of favorable outcomes (red or jacks) by the total number of outcomes (52 cards) in the deck.
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 28 / 52
So, the probability of drawing a card that is either red or a jack is 28/52, which can be simplified to 7/13.
May your luck be as colorful as a clown's wig!
To find the probability that the card is red or a jack, we need to determine the total number of favorable outcomes and divide it by the total number of possible outcomes.
First, let's determine the total number of favorable outcomes.
1. Red cards: There are 26 red cards in a standard deck (two red suits: hearts and diamonds), so the number of favorable outcomes for red cards is 26.
2. Jacks: There are 4 jacks in a standard deck (one jack in each suit), so the number of favorable outcomes for jacks is 4.
Since the red cards and jacks are inclusive, we need to subtract the duplicate jack of hearts, which we've already counted as a red card. Thus, the total number of favorable outcomes for red or jack cards is 26 + 4 - 1 = 29.
Next, let's determine the total number of possible outcomes.
In a standard deck, there are 52 cards in total.
Therefore, the probability of drawing a red card or a jack is:
P(red or jack) = (number of favorable outcomes) / (number of possible outcomes)
= 29 / 52
Simplifying, we find:
P(red or jack) ≈ 0.5577
So, the probability that the card drawn is red or a jack is approximately 0.5577 or 55.77%.
To find the probability that the card is red or a jack, we need to determine the total number of favorable outcomes and the total number of possible outcomes.
There are 52 cards in a standard deck, and half of them are red (26 red cards) and there are 4 jacks in the deck. However, we need to account for the case when a card is both red and a jack to avoid double-counting. There are 2 red jacks in the deck (the jack of diamonds and the jack of hearts).
To calculate the probability, we combine the number of red cards (26) with the number of jacks (4) and subtract the number of cards that are both red and jacks (2). This results in a total of 28 cards that are either red or jacks.
So the probability of drawing a red card or a jack is 28 divided by the total number of cards in the deck (52):
P(red or jack) = 28/52 = 7/13 ≈ 0.5385 = 53.85% (rounded to two decimal places).
Therefore, the probability of drawing a red card or a jack from a shuffled standard deck of cards is approximately 53.85%.