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forsale [732]
3 years ago
9

Five distinct numbers are randomly distributed to players numbers 1 through 5. Whenever two playerscompare their numbers, the on

e with the higher one is declared the winner. Initially, players 1 and 2compare their numbers; the winner then compares her number with that of player 3, and so on. LetXdenote the number of times player 1 is a winner.
Mathematics
1 answer:
ad-work [718]3 years ago
7 0

Answer:

Observe that the first and the second player have equal probability to get any of number. Using the principle of that symmetry, we have that  

P(X=0)=\frac{1}{2}

<u>Event X = 1 </u>means that the first player has got greater number than the second player, but not than the third player. So, choose any three numbers out of five of them and say that the minimal number out of these three goes to the second player, mean number to the first one and the largest to the third one. Permute remaining two numbers on remaining two people. Hence

P(X=1)=\frac{1}{6}

<u>Event X = 2</u> means that the first player has got greater number than the second and the third player, but not than the fourth player. So, choose any four numbers out of five of them and say that the minimal number and the next minimal out of these four go to the second and the third player (and permute them), third number to the first one and the largest to the fourth player. Give remaining number to the last person. Hence

P(X=2)=\frac{1}{12}

<u>Event X = 3</u> means that the first player has got greater number than the second, the third, and the forth player, but not than the fifth player. So, permute these five numbers as follows: give the highest to the last person, the second highest to the first, and permute remaining numbers on the remaining people. Hence  

P(X=3)=\frac{1}{20}

<u>Event X = 4</u> means basically the first player has won all the battles i.e, he has got the greatest number. Hence

P(X=4)=\frac{1}{5}

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15. a)
frutty [35]

Answer:

The correct answer is - A)8% B) 3%

Step-by-step explanation:

A) Let assume:

the cost price of the goods - $y.

the selling price of the goods - $x.

Given: The retailer sold at 4% discount, or 0.96x (100% - 4% = 96%). Since the goods were sold to make 20% profit, therefore it was sold for:

1.2y (100% + 20% = 120%).

Solution:

The refrigerator was sold at 13% VAT at Rs. 10848:

then,

=> 1.2y + 13%(1.2y) = 10848

=> 1.2y + 0.156y = 10848

=> 1.356y = 10848

=> y = 8000

Thus, the cp is Rs 8000.

The selling price is:

=> 0.96x = 1.2y

=> 0.96x = 1.2(8000)

=> x = 10000

The sp is Rs. 10000

For a profit of 15%, that is 1.15(8000) = 9200, the discount is:

(1 - discount)10000 = 9200

1 - discount = 0.92

Discount = 1 - 0.92 = 0.08 or 8%

B) Let C & M as cost price & marked price of the scanner machine respectively.  

(1 + 20/100)*C = 41400

or (6/5)*C = 41400

or C = (5/6)*41400

= 34500 (Rs)

(1 - 10/100)*(1 + 15/100)*M = 41400

or (9/10)*(23/20)*M = 41400

or M = (10/9)*(20/23)*41400

= 40000 (Rs)

Let R% as the reduction in the percent in discount  

(1 - 10/100 + R/100)*(1 + 15/100)*M

= (1 + 20/100 + 4/100)*C

or (9/10 + R/100)*(23/20)*40000

= (31/25)*34500

or 9/10 + R/100

= (20/23)(31/25)*(345/400)

or R/100 = 0.93 - 0.9 = 0.03

or R = 3%

7 0
3 years ago
Choose the correct product of (6x − 2)(6x + 2). (1 point)
Vanyuwa [196]
You did not give any choices but this can easily be solved using the FOIL method. 

FOIL stands for First, Outside, Inside, Last. 

In your equation you have (6x-2)(6x+2)
You will multiply the terms that correspond to each letter 

First: Means first terms of each set. In this case 6x and 6x
6x x 6x = 36x^{2} Now you have your first term in the sequence.

Outside: Means terms found in the outside areas of the whole equation, in this case it is 6x and 2
6x x 2 = 12x Now this is the second term

Inside: Means terms found in the inside areas of the whole equation, in this case it is -2 and 6x
-2 x 6x = -12x Now this is your third term

Last: Means the last terms of each set. In this case it is -2 and 2
-2 x 2 = -4  This is your last term

Now you have what you need for your new equation:

36x^{2} + 12x -12x - 4

Because your second and third terms are like terms, you can combine them by doing the operation indicated. 12x-12x = 0 so now you can cancel it out from your equation and your left with:

36 x^{2} - 4 This is your product
6 0
3 years ago
A gumball machine has just been filled with 50 black, 150 white, 100 red and 100 yellow gum balls that have been thoroughly mixe
Andrew [12]
<span>Exactly 33/532, or about 6.2% This is a conditional probability, So what we're looking for is the probability of 2 gumballs being selected both being red. So let's pick the first gumball. There is a total of 50+150+100+100 = 400 gumballs in the machine. Of them, 100 of the gumballs are red. So there's a 100/400 = 1/4 probability of the 1st gumball selected being red. Now there's only 399 gumballs in the machine and the probability of selecting another red one is 99/399 = 33/133. So the combined probability of both of the 1st 2 gumballs being red is 1/4 * 33/133 = 33/532, or about 0.062030075 = 6.2%</span>
6 0
3 years ago
A lottery has 60 numbers. To win the jackpot one needs to match all 7 numbers that are drawn by the machine. Is this a PERMUTATI
Vadim26 [7]

Answer: Hence, our required probability is \dfrac{1}{386206920}

Step-by-step explanation:

Since we have given that

Numbers in a lottery = 60

Numbers to win the jackpot = 7 numbers

We need to find the probability to hit the jackpot:

So, our required probability is given by

P=\dfrac{^7C_7}{^{60}C_7}\\\\P=\dfrac{1}{386206920}

This is a combination problem as we need to select 7 numbers irrespective of any arrangements.

Hence, our required probability is [tex]\dfrac{1}{386206920}[/tex

4 0
3 years ago
Determine which system below will produce infinitely many solutions. (2 points)
disa [49]
The only system that has infinitely many solutions is NUMBER 2. Where you solve a system, and both sides end up being 0=0, then the system will have infinitely many solutions. Well, in these four choices, Number 2 is the only one that ends up being 0=0 after I solved it.
6 0
3 years ago
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