Answer:
Step-by-step explanation:
We are given the two functions:
And we want to find:
This is equivalent to:
Then by substitution:
Evaluate:
Therefore:
Cards are drawn, one at a time, from a standard deck; each card is replaced before the next one is drawn. Let X be the number of draws necessary to get an ace. Find E(X) is given in the following way
Step-by-step explanation:
- From a standard deck of cards, one card is drawn. What is the probability that the card is black and a
jack? P(Black and Jack) P(Black) = 26/52 or ½ , P(Jack) is 4/52 or 1/13 so P(Black and Jack) = ½ * 1/13 = 1/26
- A standard deck of cards is shuffled and one card is drawn. Find the probability that the card is a queen
or an ace.
P(Q or A) = P(Q) = 4/52 or 1/13 + P(A) = 4/52 or 1/13 = 1/13 + 1/13 = 2/13
- WITHOUT REPLACEMENT: If you draw two cards from the deck without replacement, what is the probability that they will both be aces?
P(AA) = (4/52)(3/51) = 1/221.
- WITHOUT REPLACEMENT: What is the probability that the second card will be an ace if the first card is a king?
P(A|K) = 4/51 since there are four aces in the deck but only 51 cards left after the king has been removed.
- WITH REPLACEMENT: Find the probability of drawing three queens in a row, with replacement. We pick a card, write down what it is, then put it back in the deck and draw again. To find the P(QQQ), we find the
probability of drawing the first queen which is 4/52.
- The probability of drawing the second queen is also 4/52 and the third is 4/52.
- We multiply these three individual probabilities together to get P(QQQ) =
- P(Q)P(Q)P(Q) = (4/52)(4/52)(4/52) = .00004 which is very small but not impossible.
- Probability of getting a royal flush = P(10 and Jack and Queen and King and Ace of the same suit)
You just add all the marbles which is 15 marbles. Then how many blue ones are there 3. So you just do blue out of the whole. So your answer is 3/15
The 82nd term would be 1,369.
First we need to find an equation to represent this sequence, which we can do by finding the common difference between terms and then comparing those multiples to the sequence.
To find the common difference we simply need to do 9 - -8 = 17, and this is the same as 26 - 9 = 17, so we know that it will be the same for the whole sequence.
Then we can write multiples of 17 above the original sequence and find the difference:
17, 34, 51
-8, 9, 26
The difference between 17 and -8 is -25, so our final equation becomes:
17n - 25
Then we just substitute in 82 as n because we’re looking for the 82nd term and we get 17(82) - 25 = 1394 - 25 = 1369
I hope this helps!