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)
Step-by-step explanation:
I am not sure I understand the answer options.
but normally the answer should be "commission".
as this is the defined way of payment, when you get paid based on the items sold.
but in any case, what math question is this ?
The ladder, leaning against the building, forms a right triangle with height "a" being the distance from the ground to the window, and hypotenuse "c" being the length of the ladder.
Because it's a right triangle, we can use trigonometric ratios to find the angles we're missing.
For part A), to solve for the angle between the base of the ladder and the ground, you'll want to use sine, because we know the lengths of the opposite side and the hypotenuse.
Sin(x) = a/c , solve for angle x in degrees or radians.
For part B), finding the angle between the top of the ladder and the building, remember that the sum of the angles in a triangle is 180 degrees, or pi radians, depending on which unit your teacher prefers.
Assuming degrees, we can say that angle y = 180-90-x. You are simply subtracting the two known angles to find the third.
For part C) use the Pythagorean theorem. You're looking for the length of the base, "b". Recall:
a^2 + b^2 = c^2
Plug in the known values, and solve for b.
Answer:
4
Step-by-step explanation:
