Please help fast !!!! I really Don't understad This i need help please its so frustrating

Suppose I ask you to pick any four cards at random from a deck of 52, without replacement, and bet you one dollar that at least

Tatiana [17]

Answer:

a) No, because you have only 33.8% of chances of winning the bet.

b) No, because you have only 44.7% of chances of winning the bet.

Step-by-step explanation:

a) Of the total amount of cards (n=52 cards) there are 12 face cards (3 face cards: Jack, Queen, or King for everyone of the 4 suits: clubs, diamonds, hearts and spades).

The probabiility of losing this bet is the sum of:

- The probability of having a face card in the first turn

- The probability of having a face card in the second turn, having a non-face card in the first turn.

- The probability of having a face card in the third turn, having a non-face card in the previous turns.

- The probability of having a face card in the fourth turn, having a non-face card in the previous turns.

1) The probability of having a face card in the first turn

In this case, the chances are 12 in 52:

$P_1=P(face\, card)=12/52=0.231$

2) The probability of having a face card in the second turn, having a non-face card in the first turn.

In this case, first we have to get a non-face card (there are 40 in the dech of 52), and then, with the rest of the cards (there are 51 left now), getting a face card:

$P_2=P(non\,face\,card)*P(face\,card)=(40/52)*(12/51)=0.769*0.235=0.181$

3) The probability of having a face card in the third turn, having a non-face card in the first and second turn.

In this case, first we have to get two consecutive non-face card, and then, with the rest of the cards, getting a face card:

$P_3=(40/52)*(39/51)*(12/50)\\\\P_3=0.769*0.765*0.240=0.141$

4) The probability of having a face card in the fourth turn, having a non-face card in the previous turns.

In this case, first we have to get three consecutive non-face card, and then, with the rest of the cards, getting a face card:

$P_4=(40/52)*(39/51)*(38/50)*(12/49)\\\\P_4=0.769*0.765*0.76*0.245=0.109$

With these four probabilities we can calculate the probability of losing this bet:

$P=P_1+P_2+P_3+P_4=0.231+0.181+0.141+0.109=0.662$

The probability of losing is 66.2%, which is the same as saying you have (1-0.662)=0.338 or 33.8% of winning chances. Losing is more probable than winning, so you should not take the bet.

b) If the bet involves 3 cards, the only difference with a) is that there is no probability of getting the face card in the fourth turn.

We can calculate the probability of losing as the sum of the first probabilities already calculated:

$P=P_1+P_2+P_3=0.231+0.181+0.141=0.553$

There is 55.3% of losing (or 44.7% of winning), so it is still not convenient to bet.

5 0

3 years ago

Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 29% each week. The following function represents

Dmitry [639]

Answer:

Option A. $f(x)=86[1.04]^{x}$ ; grows approximately at a rate of 0.4% daily

Step-by-step explanation:

we have

$f(x)=86(1.29)^{x}$

where

f(x) the number of weeds in the garden

x ----> the number of weeks

Calculate how quickly the weeds grow each day

Remember that a week is equal to seven days

so

$f(x)=86(1.29)^{\frac{x}{7}}$

Using the law of exponents

b^(x/a) = b^(x*(1/a)) = (b^(1/a))^x

so

$f(x)=86[(1.29)^{\frac{1}{7}}]^{x}$

$f(x)=86[1.04]^{x}$

therefore

The rate is approximately

1.04=1+r

r=1.04-1=0.04=4% daily

8 0

3 years ago

Where does the parentheses go in 3+6 ×9+3 to made a total of 84

chubhunter [2.5K]

Answer:

Around the 3 + 6:-

(3 + 6) x 9 + 3

Step-by-step explanation:

(3 + 6) x 9 + 3

= 9 x 9 + 3

= 84.

4 0

3 years ago

Read 2 more answers

I NEED HELP !!!!!!!!!!!!!!!!!

Mama L [17]

Answer:

Read

Step-by-step explanation:

4 0

3 years ago

You are making a scaledrawing of a room using a scale of1 inch : 4 feet.a. The room is 14 feet by 18 feet. Find itsdimensions in

lilavasa [31]

Answer:

a. 3.5 inches by 4.5 inches

b. 1.5 inches

c. Divide 48 inches by 2 and multiply 1 inch by 12 to get a scale of 1 : 2

Step-by-step explanation:

A scale is a representative fraction showing the relationship between length on a drawing and actual length.

i.e scale = $\frac{length on a drawing}{actual length}$

scale = 1 inch : 4 feet

a. The dimensions in the drawing can be determined as;

1 inch : 4 feet implies an inch on the drawing equates 4 feet on actual length.

$\frac{14}{4}$ = 3.5 inches

$\frac{18}{4}$ = 4.5 inches

Dimensions on drawing is 3.5 inches by 4.5 inches.

b. The length of the sofa is 6 feet, its length on the drawing is;

$\frac{6}{4}$ = 1.5 inches

c. To enlarge the scale so as to double the dimensions of the drawing, we have;

12 inches = 1 feet

4 feet = 4 × 12 = 48 inches

given scale = 1 inch : 48 inches

Thus, divide 48 inches by 2 and multiply 1 inch by 12.

scale = 12 inch : 24 inch

scale = 1 : 2

To double the dimensions of the drawing, the scale required is 1 : 2. This implies that a unit measure on the drawing is synonymous to 2 measures on the actual reading.

6 0

3 years ago