Use the distributive property to write an equivalent expression. 8(10p + 6q

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

Three friends compared their last math test. San got 13/15, John got 69% and Phillip got 12/18. Put their grades in order from h

Elodia [21]

San 13/15, John 69%, Phillip 12/18. When you divide 13/15 you'll get 86. When you divide 12/18 you'll get 66.

5 0

3 years ago

A shadow 60 meters long is cast by a stone tower that is 32 meters tall. If a cedar tree close

hjlf

Answer:

107

Step-by-step explanation:

you will add 60 + 32 +15 = 107 that is how i got the answer

6 0

3 years ago

The distance on a bike path between Westfield and Southborough is 46 mi. Tracey leaves Westfield heading to Southborough cycling

ipn [44]

Answer: 2 hr.

Explanation: Think back to rate of change. d = rt, r = d/t, t = d/r. In this case, we will be using d = rt. Mph would be r, rate, so you would categorize 15 mph and 8 mph under rate. t should represent the time each cyclist traveled. Tracey's and Emma's distance, d, would be the same as their mph, hence Tracey's being 15t and Emma's would be 8t. When you add Tracey's distance plus Emma's distance, you end up with 46 mi. Now, you need to combine like terms, which should look like 15t + 8t = 46. Add 15 and 8 to get 23, so it should be 23t = 46 now. Then, divide both sides of the equation by 23 and now you should have your answer, t = 2 hr.

8 0

3 years ago

Read 2 more answers

seven students took a bus to the State Park. The round-trip tickets cost $45 per student. They stayed for a few nights at a camp

vladimir2022 [97]

You need to know how much the state Park camping cost, I think...

4 0

3 years ago

Use the distributive property to write an equivalent expression. 8(10p + 6q - 1)​

Use the distributive property to write an equivalent expression. 8(10p + 6q - 1)