Can someone please help me for this question

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 = $\frac{3}{1081} + \frac{6}{1081}$

= $\frac{9}{1081}$ = 0.0083.

3 0

3 years ago

Read 2 more answers

The equation y = 8.1x models the relationship between the number of hours Alexander works, x, and the dollar amount he earns, y.

Katarina [22]

Start the graph at the y-intercept. At 0 hours, he will make $0, so (0, 0) is the y-intercept. From this point, he makes $8.10 an hour; go up 8.1 for every 1 hour you go over on the graph. The graph is attached.

4 0

2 years ago

Read 3 more answers

I need help with his problem with details.

inysia [295]

Answer:

The solution is y> -1

Step-by-step explanation:

y- 6 > -7

y> -7+6 (add 6 on both sides)

y> -1

The graph should the the first option from the right, with the dot above -1.

Since y is greater than -1, the dot should be on -1 and the arrow should be pointing towards the right. It shouldn't be a coloured dot because the sign is 'greater than' (>) not 'greater or equal to' (≥)

5 0

3 years ago

The diagram shows a row of five identical tiles each in the shape of an isosceles trapezoid what is the area of one tile

Misha Larkins [42]

Get the total amount of the 5 tiles and divide it by 5.

5 0

3 years ago

Put this equation into slope intercept -2×+3y=9

siniylev [52]

y = $\frac{2}{3}$ x + 3

The equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange - 2x + 3y = 9 into this form

add 2x to both sides

3y = 2x + 9 ( divide all terms by 3 )

y = $\frac{2}{3}$ x + 3 ← in slope-intercept form

6 0

3 years ago

Can someone please help me for this question​

Can someone please help me for this question