I need help with this plz

Five cards are drawn from a standard 52-card playing deck. A gambler has been dealt five cards—two aces, one king, one 3, and on

Nookie1986 [14]

Answer:

The probability that he ends up with a full house is 0.0083.

Step-by-step explanation:

We are given that a gambler has been dealt five cards—two aces, one king, one 3, and one 6. He discards the 3 and the 6 and is dealt two more cards.

We have to find the probability that he ends up with a full house (3 cards of one kind, 2 cards of another kind).

We know that gambler will end up with a full house in two different ways (knowing that he has given two more cards);

If he is given with two kings.
If he is given one king and one ace.

Only in these two situations, he will end up with a full house.

Now, there are three kings and two aces left which means at the time of drawing cards from the deck, the available cards will be 47.

So, the ways in which we can draw two kings from available three kings is given by = $\frac{^{3}C_2 }{^{47}C_2}$ {∵ one king is already there}

= $\frac{3!}{2! \times 1!}\times \frac{2! \times 45!}{47!}$ {∵ $^{n}C_r = \frac{n!}{r! \times (n-r)!}$ }

= $\frac{3}{1081}$ = 0.0028

Similarly, the ways in which one king and one ace can be drawn from available 3 kings and 2 aces is given by = $\frac{^{3}C_1 \times ^{2}C_1 }{^{47}C_2}$

= $\frac{3!}{1! \times 2!}\times \frac{2!}{1! \times 1!} \times \frac{2! \times 45!}{47!}$

= $\frac{6}{1081}$ = 0.0055

Now, probability that he ends up with a full house = $\frac{3}{1081} + \frac{6}{1081}$

= $\frac{9}{1081}$ = <u>0.0083</u>.

3 0

3 years ago

Read 2 more answers

The same player is going to play the game 200 times consecutively. How many black balls should he expect to pick

DerKrebs [107]

Answer:

200

Step-by-step explanation:

It is given that the same player is going to play a game one after another continuously about 200 times. During the game the player is going to pick up black color balls.

If the player picks at least one black color ball at one time of the game, therefore, the probability of the number of black balls that the player is going to pick is 200 balls.

8 0

3 years ago

Mary said that the temperature outside on two differnt days had an absolute value 20. Kate said she was wrong because the temper

TiliK225 [7]

Answer:

Mary is correct we don’t know the temperature but it can be implied that one is 20 and the other is -20 because of absolute value which is the distance a number away from zero that means that you have two answers or two days in this case that both have an absolute value of 20

Step-by-step explanation:

5 0

3 years ago

The perimeter of a picture frame is 24 inches. If the width of the picture frame is 5 inches, what is the length of the picture

Zarrin [17]

L=7
2l+2w=24
2l+2x5=24
2l+10=24
2l=14
l=7

3 0

3 years ago

Read 2 more answers

A student says that the graph of the equation y=3(x+8) is the same as the graph of y=3x, only translated upwards by 8 units. do

tino4ka555 [31]

Answer: