# Math

A game is played by throwing darts at a target. A player can choose to throw two or three darts.

Darcy plays two games. In Game 1, he chooses to throw two darts, and wins if he hits the target at least once. In Game 2, he chooses to throw three darts, and wins if he hits the target at least twice.

The probability that Darcy hits the target on any throw is p, where 0 < p < 1.

(i) Show that the probability that Darcy wins Game 1 is 2p - p[squared].

(ii) Show that the probaility that Darcy wins Game 2 is 3p[squared] - 2p[cubed].

(iii) Prove that Darcy is more likely to win Game 1 than Game 2.

(iv) Find the value of p for which Darcy is twice as likely to wine Game 1 as he is to win Game 2.

1. 👍 0
2. 👎 0
3. 👁 292
1. pr(win)=1-pr(lose)=1-(1-p)(1-p)

ii pr (win)=p*P(1-P)

iii is 2P-P^2>p^2-p^3 ?
divide by p
2-p>? P-P^2

2-2p+P^2>?0
(2-P)(1-P)>?0
because p is between zero and 1, then each of the two terms on the left is positive, so the left side is indeed greater than zero.

1. 👍 0
2. 👎 0
👨‍🏫
bobpursley

## Similar Questions

1. ### Statistics

Suppose a basketball player is an excellent free throw shooter and makes 90% of his free throws (i.e., he has a 90% chance of making a single free throw). Assume that free throw shots are independent of one another. Suppose this

2. ### Physics

A ball player catches a ball 3.33s after throwing it vertically upward. a) with what speed did he throw it? b) what height did it reach?

3. ### math

Some friends played a board game. During the​ game, one unlucky player had to move back 9 spaces 7 turns in a row. Find a number to represent that​ player's movements for those 7 turns. The number nothing represents that​

4. ### math

If a basketball player consistently shoots 80% from the free throw line and she takes 25 free throw shots throughout the course of a game, how many free throws can she be expected to make?

1. ### math

juana threw five darts at a dartboard. the possible scores on a target were 2,4,6,8 and 10. each dart hit the target. which of these total score can be identified as "not possible": 38,23,58,30,42,31,26,6,14, or 15?

2. ### Statistics

A game is played using one die. There is a\$1 charge to play the game. If the die is rolled and shows a five, the player receives \$6 back ( a profit of \$5 and the original \$1). If any other number shows, theplayer loses the

3. ### Math

Thomas and Jonelle are playing darts in their garage using the board with the point values for each region shown below. The radius of the outside circle is 10 inches, and each of the other circles has a radius 2 inches smaller

4. ### Math

If exactly three darts hit this target, how many different scores are possible? darts circle 1 3 5

1. ### math

Some friends played a board game. During the​ game, one unlucky player had to move back spaces turns in a row. Find a number to represent that​ player's movements for those turns. The number nothing represents that​ player's

2. ### P.E check my answers

1.Select the community activity that is a healthy choice to promote fitness for all ages A.annual 5K fun run for charity

3. ### 8th grade

Jamie was throwing darts at targets. When his dart landed in the center of the target(the bull eye)and he earned 7 points. However, when his dart landed on the outside ring he earned 2 points. After 50 throws his friend reported

4. ### Math

You are throwing darts at a dart board. You have a 1/6 chance of striking the bull's-eye each time you throw. If you throw 3 times, what is the probability that you will strike the bull's-eye all 3 times?