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4 years ago

Two cards are dealt at random from a standard 52 card deck (without replacement). (Ace, King, Queen, Jack are face cards.)

Mathematics

1 answer:

Tema [17]4 years ago

7 0

Answer:

The answer is below

Step-by-step explanation:

There are 52 cards in a deck, 12 of these cards are face cards (4 kings, 4 queens and 4 jacks) and 40 are not face cards

a. Find the probability that the first card is a face card and the second is NOT a face card.

There are 12 first card, the probability that the first card is a face card is 12/52.

Since there are no replacement, after picking 1 face card the number of cards remaining is 51, the probability of the second card not being a face card = 40/51. Therefore:

The probability that the first card is a face card and the second is NOT a face card = P(first is face card) × P(second is not face card) = 12/52 × 40/51 = 40/221

b) Find the probability that they are both face cards.

The probability that the first card is a face card is 12/52.

Since there are no replacement, after picking 1 face card the number of cards remaining is 51 and the number of face card remaining is 11, the probability of the second card is a face card = 11/51. Therefore:

The probability that they are both face cards = P(first is face card) × P(second is face card) = 12/52 × 11/51 = 11/221

c) Find the probability that the second is a face card given the first is NOT a face card.

The probability that the first card is not a face card = 40/52

Since there are no replacement, after picking the first card the number of cards remaining is, the probability of the second card is a face card = 12/51. Therefore:

The probability that the second is a face card given the first is NOT a face card = P(first is not a face card) × P(second is face card) = 40/52 × 12/51 = 40/221

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Given cosine of x = $-\frac{\sqrt{3} }{2}$

i.e., cos(x) = $-\frac{\sqrt{3} }{2}$

Also cos( $\frac{\pi}{6}$ ) = $\frac{\sqrt{3} }{2}$ . So x = $\frac{\pi}{6}$ .

We need to find cos(x+π) = cos( $\frac{7\pi}{6}$ ).

But its value is not easy to find. So we use trigonometric formulas.

We have the trigonometric formula, cos (x+π) = - cos(x) = - $-\frac{\sqrt{3} }{2}$ = $\bold{\frac{\sqrt{3} }{2}}$

Cos(x+π) lies in the 3rd quadrant. So there cosine has negative values. That is why, cos (x+π) = - cos(x).

Learn more about Cos(x+π) trigonometric formula at brainly.com/question/12243383

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2 years ago

You divided 2/3 of a gallon of paint equally among 4 containers. How much paint is in each container.

Hunter-Best [27]

Answer:

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Step-by-step explanation:

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2 years ago

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Rudiy27

Answer:

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Step-by-step explanation:

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3 years ago

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T= # of years= 10

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divide inside parentheses first

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add inside parentheses

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multiply exponents

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multiply parentheses by exponents

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3 years ago

PLEASE HELP! Given the following equation of an exponential function N= 40.25(1.0394)^t determine the base, b, of the exponentia

NeTakaya

The exponential equation in its generic form is:
y = A * (b) ^ t
Where,
A: initial amount
b: base (Growth rate for b> 1. Decrease rate for b <1.)
t: time.
We have then that the equation is:
N = 40.25 (1.0394) ^ t
The base is:
b = 1.0394> 1 (it is a growth rate)
Answer:
The base, b, of the exponential model is:
b = 1.0394
the base is a growth rate

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3 years ago