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NISA [10]
1 year ago
12

In a two-player game, five cards, numbered 1 through 5, are placed in a bag. A card is drawn at random, and the players look at

the number. Which of the following scoring rules makes a fair game?
If it is greater than 2, Player 1 earns 2 points. If not, Player 2 earns 2 points.

If it is less than 2, Player 1 earns 3 points. If not, Player 2 earns 2 points.

If it is greater than 3, Player 1 earns 2 points. If not, Player 2 earns 2 points.

If it is less than 3, Player 1 earns 3 points. If not, Player 2 earns 2 points.
Mathematics
2 answers:
IceJOKER [234]1 year ago
8 0

Answer:

If it is less than 3, Player 1 earns 3 points.

If not, Player 2 earns 2 points.

Step-by-step explanation:

<u>Player 1</u> :

p(N < 3) = p(N = 1 or N = 2) = 2/5

<u>Player 2</u> :

p(N ≥ 3) = p(N = 3 or N = 4 or N = 5) = 3/5

<u>We notice that</u> :

p(N < 3) × 3 = (2/5) × 3 = 6/5

On the other hand,

p(N ≥ 3) × 2 = (3/5) × 2 = 6/5

since ,the probability player 1 win multiplied by the associated number of points (3)

is equal to

the probability player 2 win multiplied by the associated number of points (2).

Then the game is fair.

Law Incorporation [45]1 year ago
5 0

Answer:

The last scoring rule makes a fair game

<em>If card value is less than 3, Player 1 earns 3 points. If not, Player 2 earns 2 points</em>.

Step-by-step explanation:

This is a question which relates to probabilities, complementary probabilities and expected outcomes

Since there are 5 cards in total and only 1 card is picked, the probability of picking a card is the same i.e. 1/5 = 0.2 since each card is identical and therefore has the same likelihood of being drawn

Let's go through each of the rules, find the associated outcomes and probabilities of each of the outcome

The attached table shows a summary of all the possible outcomes of each rule, the probabilities associated with it, the complement of the rule, the complement probability, expected payoffs and who has the advantage for each rule

As an example, take the first row relating to the first rule:
If value of card is greater than 2, Player 1 earns 2 points. If not, Player 2 earns 2 points.

If the value is greater than 2 then the value is either {3, 4 or 5}. There are 3 possible outcomes out of a total of 5 so,

P(card value > 2) = P(3, 4, 5) = 3/5 = 0.6   and Player 1 gets 2 points so the expected value = 0.6 x 2 = 1.2 EP(P1

The complement of this event is

card value <=2 ie card value is either 1 or 2 ie 2 possible out of 5
P(card value <=2) = P(1,2) = 2/5 = 0.4
Note that this probability is 1 - P(card value > 2) = 1- 0.6 = 0.4

If so, Player 2 gets 2 points and his/her expected payoff is 0.4 x 2 = 0.8 EP(P2)

Since EP(P1) > EP(P2) this rule gives player 1 an advantage and therefore not a fair game

The other rows of the table can be interpreted the same way. Essentially we are looking for a rule that gives both players the same expected payoff and therefore each player has the same chance of winning

The table shows that the last rule is the fairest

 

   

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Stefan sells Jin a bicycle for $163 and a helmet for $17. The total cost for Jin is 150% of what Stefan spent originally to buy
cluponka [151]

Answer:

44$

Step-by-step explanation:

4 0
2 years ago
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A cannon ball is launched at 6 feet per second from the top of a platform 12 feet above the ground.
AleksAgata [21]
A.) y = ut - 1/2gt^2 + 12
y = 6t - 1/2(9.8)t^2 + 12
y = 6t - 4.9t^2 + 12

b.) The y-intercept is 12

c.) The y-intercept represent the height of the ball at time t = 0

d.) At the time the ball reaches the ground, y = 0
-4.9t^2 + 6t + 12 = 0
t = 2.29 seconds
Therefore, it took the ball 2.29 seconds to reach the ground.
7 0
3 years ago
Find the sum of
Mars2501 [29]

If I read it right then 1. -147

2. -100

4 0
3 years ago
Find the distance between A (6, -1) and B ( -18, 15)
timama [110]

Answer:

8√13 units

Step-by-step explanation:

We use the distance formula.

The distance formula states that the distance between two points (x, y) and (a, b) is equal to:

d = \sqrt{(x-a)^2+(y-b)^2}

Here, x = 6, y = -1, a = -18, and b = 15. Plug these in:

d = \sqrt{(x-a)^2+(y-b)^2}

d = \sqrt{(6-(-18))^2+(-1-15)^2}=\sqrt{24^2+(-16)^2} =\sqrt{576 + 256} =\sqrt{832} = 8√13

The answer is thus 8√13 units.

<em>~ an aesthetics lover</em>

7 0
3 years ago
Read 2 more answers
For every 5 pages in a book Fred reads, Lonnie reads 4 pages. In 1 hour, they read a combined total of 36 pages. How many pages
nydimaria [60]

Answer:

Hence the number of pages read by Lonnie is 16 pages when they read a combined of 36 pages.

Step-by-step explanation:

The table that can be formed by the rate at which they study the number of pages of a book is:

Fred     Lonnie       total

 5           4                9

 10          8               18

 15          12              27

 20         16              36

That means when they read a combined of 36 pages.

Then the number of pages read by Fred is 20 pages.

and the number of pages read by Lonnie is 16 pages.

(

Also it could be done as :

Let Fred reads 'x' pages.

so, the number of pages read by Lonnie is: (4/5)x

Hence,

x+(4/5)x=36

on solving this linear equation we have:

x=20

and (4/5)x=16

)

Hence the number of pages read by Lonnie is 16 pages when they read a combined of 36 pages.

3 0
3 years ago
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