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)
X=15
expand the brackets and collect like terms so 6x+15=7x
then -6x to get x=15
g(f(x)) means plug in f(x) for every "x" in g(x).
g(f(x))=(x+4)^2-1=x^2+8x+16-1=x^2+8x+15
answer: x^2+8x+15
Answer:
20
Step-by-step explanation:
Given :
Length = l
Width = w
Area of square = 45
Let side of square = x
Area of square = x²
45 = x²
√45 = x
l of rectangle = x + 5 = √45 + 5
w of rectangle = x -5 = √45 -5
Area of rectangle= l * w
Area = (√45 + 5) * (√45 - 5)
Area = 45 - 5√45 + 5√45 -25
Area = 45 -25
Area of rectangle = 20
-5 is the answer
-11-(-6)= -5
