Which of the following are solutions to ? Check all that apply.

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

Alberto is painting a large triangle on one wall of his bedroom. The base of the triangle is 4 ft, and the height is 8 ft. It ta

N76 [4]

Answer: 3.2 qts

Step-by-step explanation:

A=1/2 * b *h

1/2 * 4*8 = 16 square foot

Area is 16 square foot

Multiply the area by the quarts of paint it takes to cover 1 square foot.

16 * 0.2 = 3.2 qts

4 0

3 years ago

You have won the lottery and will receive 20 annual payments of $10,000 starting today. If you can invest these payments at 8.5%

xxTIMURxx [149]

Answer:

$102,677.20

Step-by-step explanation:

The present value of an annuity due is determined by the following expression:

$PV = P+P*(\frac{1-(1+r)^{-n+1}}{r})$

Where 'P' is the amount of each payment received, 'r' is the interest rate on the investment and 'n' is the number of yearly payments.

With 20 annual payments of $10,000 at a rate of 8.5%, the present value is:

$PV = 10,000+10,000*(\frac{1-(1+0.085)^{-20+1}}{0.085})\\PV = 10,000+ 10,000*(9.26772)\\PV=\$102,677.20$

The present value of your winnings is $102,677.20.

8 0

2 years ago

Procedure for this problem -8+(-24)

lana66690 [7]

Answer: - 32

Step-by-step explanation:

-8 + (-24)

Infront of the Positive is a one.

-8 +1 (-24)

If we follow order of operations which is parentheses, exponents, multiply divide, add, and subtract, we can see we need to multiply/ distribute first. And a positive times a negative is a negative.

-8 -24

Now we put the two numbers together.

-32

This is the answer

6 0

2 years ago

Write an inequality for the sentence below and then solve and check it. The sum of w and nine is less than 18

Andre45 [30]

Answer:

w < 9

Step-by-step explanation:

w + 9 < 18

To solve this inequality, we MUST get the w by itself

Subtraction Property of Equality w + 9 - 9 < 18 - 9

Answer w < 9

7 0

2 years ago