two cards are dealt in succession from a standard deck of cards. find the probability that the first card is a diamond or a king.
probability that the second card is red given that the first card was a heart.
if two dice are rolled, what is the probability of rolling at least one three?
i have 2c1(5/6)^1(1/6)^1+2c2(5/6)^1(1/6)^2 but what do i do after this. can someone please explain in regular terms, NOT math terms! thanks :)
f(x)=x+5, g(x)=x^2-2x+1
f(2)-g(2)..how do i do this????
The first card has a 1/4 chance of being a diamond. Since the phrase is "or," it now excludes all diamonds, including the king of diamonds. So now the chances of getting a king are 3 kings out of the remaining 39 cards. In an "either-or" situation you add the individual probabilities of the specific events.
There is a 1/4 chance of getting a heart on the first card. Without replacement, the chances of getting a red card are 25 out of the remaining 51 cards. Since you want to know the probability of "both/all" events occurring, you multiply the individual probabilities.
"At least one three" means one three or two threes. Since each die has 6 sides, the probability = 1/6 + 1/36. ("either-or" again)
I hope this helps. Thanks for asking.
To find the probability that the first card is a diamond or a king, we need to determine the total number of favorable outcomes and the total number of possible outcomes.
1. Total number of favorable outcomes: In a standard deck of cards, there are 13 diamonds (one for each value: Ace, 2-10, Jack, Queen, and King) and 4 kings (one for each suit: heart, diamond, clubs, and spades). However, one king is already counted as a diamond. So, we have 12 diamond cards and 3 additional king cards. Therefore, the total number of favorable outcomes is 12 + 3 = 15.
2. Total number of possible outcomes: In a standard deck, there are 52 cards in total.
So, the probability of the first card being a diamond or a king is: 15/52, which simplifies to 5/17.
To find the probability that the second card is red given that the first card was a heart, we need to consider the cards that are left in the deck and determine the number of favorable outcomes.
1. Remaining cards: After drawing the first card (a heart), we are left with 51 cards in the deck. Out of these, 26 cards are red (diamonds and hearts) and 25 cards are black (spades and clubs).
2. Total number of favorable outcomes: In this case, we are interested in the second card being red, given that the first card was a heart. So, in the remaining 51 cards, there are 25 red cards.
Therefore, the probability of the second card being red, given that the first card was a heart, is: 25/51.
For rolling two dice and finding the probability of rolling at least one three, we need to consider the possible outcomes and determine the number of favorable outcomes.
1. Total number of outcomes: When two dice are rolled simultaneously, there are 36 possible outcomes. Each die has 6 sides (numbered 1 to 6), so the total number of outcomes is 6 (for the first die) multiplied by 6 (for the second die), resulting in 36 total outcomes.
2. Total number of favorable outcomes: To count favorable outcomes, we need to determine the number of outcomes where at least one dice shows a three.
- Outcomes where both dice show three: There is only one way for both dice to show a three (3, 3).
- Outcomes where only one dice shows three: There are two ways for one die to show a three (3, 1) and (1, 3).
So, there are three favorable outcomes.
Therefore, the probability of rolling at least one three is: 3/36, which simplifies to 1/12.
To evaluate f(2) - g(2), we substitute the value of 2 into each function and then subtract the resulting values.
1. Evaluating f(2): Substitute x = 2 into f(x) = x + 5.
- f(2) = 2 + 5
- f(2) = 7
2. Evaluating g(2): Substitute x = 2 into g(x) = x^2 - 2x + 1.
- g(2) = 2^2 - 2(2) + 1
- g(2) = 4 - 4 + 1
- g(2) = 1
Finally, we subtract the value of g(2) from f(2):
- f(2) - g(2) = 7 - 1
- f(2) - g(2) = 6