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jarptica [38.1K]
3 years ago
8

A standard deck of cards has 52 cards, 4 of each type (Ace, King, Queen, Jack, 10,...,2). From a well-shuffled deck, you are dea

lt a hand of 5 cards (without replacement).
(a) What is the probability that you are dealt at least one face card (that is a king, queen or jack)?
(b) What is the probability that you are dealt with both; at least one ace and at least one face card?
Mathematics
1 answer:
Wewaii [24]3 years ago
3 0

Answer:

a)%85,5

b)%92,2

Step-by-step explanation:

a) To determine the probability of getting a hand with at least one face, we need to calculate the probability of the hand without any face firstly.

(36/52)*(35/51)*(34/50)*(33/49)*(32/48)=0,145

Then, we need to deduct this value from the probability 1

1-0,145=0,855

The probability of the hand with at least one face is %85,5.

b)To determine the probability of a hand with at least one ace and face we will track the same road again.

(32/52)*(31/51)*(30/50)*(29/49)*(28/48)=0,0775

Then, we need to deduct this value from the probability 1

1-0,0775=0,922

The probability of the hand with at least one ace and one face is %92,2.

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Answer:

Option C) 0.2358

Step-by-step explanation:

We are given the following data set:

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Formula:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.  

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{3.39675}{6} = 0.566125

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S.D = \sqrt{\frac{0.2784182787}{5}} = 0.2358

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Option C) 0.2358

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Answer:

The worth of the car after 6 years is £2,134.82

Step-by-step explanation:

The amount at which Dan buys the car, PV = £2200

The rate at which the car depreciates, r = -0.5%

The car's worth, 'FV', in 6 years is given as follows;

FV = PV \cdot \left ( 1 + \dfrac{r}{100} \right )^n

Where;

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FV = The future value of the asset

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n = The number of years (depreciating) = 6

By plugging in the values, we get;

FV = 2200 \times \left ( 1 + \dfrac{-0.5}{100} \right )^6 \approx 2,134.82

The amount the car will be worth which is its future value, FV after 6 years is FV ≈ £2,134.82 (after rounding to the nearest penny (hundredth))

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