Suppose Ari loses 31 ​% of all ping dash pong games . ​(a) What is the probability that Ari loses two ping dash pong games in a​ row? ​(b) What is the probability that Ari loses six ping dash pong games in a​ row? ​(c) When events are​ independent, their complements are independent as well. Use this result to determine the probability that Ari loses six ping dash pong games in a​ row, but does not lose seven in a row.

​(a) The probability that Ari loses two ping dash pong games in a row is . 0961 . ​(Round to four decimal places as​ needed.) ​(.31)^2

(b) The probability that Ari loses six ping dash pong games in a row is . 0009 . ​(Round to four decimal places as​ needed.) ​(.31)^6

(c) The probability that Ari loses six ping dash pong games in a​ row, but does not lose seven in a row is nothing . ​(Round to four decimal places as​ needed.)

In python 3.7:

You’re going to program a simulation of the following game. Like many probability games, this one involves an infinite supply of ping-pong balls. No, this game is "not quite beer pong."

The balls are numbered 1 through N. There is also a group of N cups, labeled 1 through N, each of which can hold an unlimited number of ping-pong balls (all numbered 1 through N). The game is played in rounds. A round is composed of two phases: throwing and pruning.

• During the throwing phase, the player takes balls randomly, one at a time, from the infinite supply and tosses them at the cups creating a stack of balls in each cup. The throwing phase is over when each cup contains at least one ping-pong ball.
• Next comes the pruning phase. During this phase the player goes through all the balls in each cup and removes any ball whose number does not match the containing cup.

Every ball drawn has a uniformly random number, every ball lands in a uniformly random cup, and every throw lands in some cup. The game is over when, after a round is completed, there are no empty cups.

After each round, print the non-empty cups and number of balls each hold.

At the end of the simulation you will print the following:

How many rounds would you used to finish this game?

How many balls did you draw and throw to finish this game?

Sort the cups in descending order by the number of balls they hold.  

only importing random, no pygame

In python please:

You’re going to program a simulation of the following game. Like many probability games, this one involves an infinite supply of ping-pong balls. No, this game is "not quite beer pong."

The balls are numbered 1 through N. There is also a group of N cups, labeled 1 through N, each of which can hold an unlimited number of ping-pong balls (a;ll numbered 1 through N). The game is played in rounds. A round is composed of two phases: throwing and pruning.

• During the throwing phase, the player takes balls randomly, one at a time, from the infinite supply and tosses them at the cups creating a stack of balls in each cup. The throwing phase is over when each cup contains at least one ping-pong ball.
• Next comes the pruning phase. During this phase the player goes through all the balls in each cup and removes any ball whose number does not match the containing cup.

Every ball drawn has a uniformly random number, every ball lands in a uniformly random cup, and every throw lands in some cup. The game is over when, after a round is completed, there are no empty cups.

At the end of the simulation you will print the following:

How many rounds would you expect to need to play to finish this game?

How many balls did you draw and throw to finish this game?

Sort the cups in descending order by the number of balls they hold.  

The diameter of a brand of​ ping-pong balls is approximately normally​ distributed, with a mean of 1.31 inches and a standard deviation of 0.04 inch. A random sample of 16 ​ping-pong balls is selected. Complete parts​ (a) through​ (d). What is the probability that the sample is between 1.28 and 1.3 ​inches?

6. A and B are playing a short game of ping pong where A serves 3 times and B also serves 3 times. If after these six points one of them is ahead the game ends, otherwise they go into a second phase. Suppose that A wins 70% of the points when they serve and 40% of the points when B serves.

Let’s look at the first phase.

a) (3 pts) Find the probability that A or B wins 0, 1, 2, or 3 points when they serve (give the answers separately, so P(A wins 0 points when A serves)= , ...).

b) (4 pts) Find the probability that A scores a total of 4 or more points (so wins in the first phase).

c) (2 pts) Find the probability that A scores 3 points in total (so there is a tie in the first phase).

Now let’s look at cases where the game moves on to the second phase. In this phase there are multiple rounds; in each round each player serves once. They win if they win both points; otherwise it goes to another round. Play continues until someone wins.

d) (4 pts) Find the probability that A wins if it goes to the second phase.

e) (2 pts) Find the probability that A wins (in either the first or second phase).

f) Extra credit (3 pts): find the expected number of points played.

B. Five bowls are labeled 1,2,3,4,5. Bowl i contains i white and 5 − i black ping pong balls, for i = 1,2,3,4,5. A bowl is randomly selected, and 2 ping pong balls are selected from that bowl at random without replacement. Both selected balls were white. What is the probability they were selected from bowl 1? 2? 3? 4? 5?

B. Five bowls are labeled 1,2,3,4,5. Bowl i contains i white and 5 − i black ping pong balls, for i = 1,2,3,4,5. A bowl is randomly selected, and 2 ping pong balls are selected from that bowl at random without replacement. Both selected balls were white. What is the probability they were selected from bowl 1? 2? 3? 4? 5?

In the daily Play 4, players select a number between 0000 and 9999. The lottery machine

contains 4 bins, each with 10 ping-pong balls. Each bin has its ping-pong balls labeled

0, 1, 2, . . . , 9. The state then “randomly” selects a ball from each bin and forms a number

between 0000 and 9999. WHAT IS THE PROBABLITIY OF WINNING PLEASE TYPE

Suppose that the balls in a large bucket of colored ping pong balls consist of 40% red balls, 50% green balls, and 10% yellow balls. Suppose that 5% of the red balls are dented, 2% of the green balls are dented, and 1% of the yellow balls are dented. Assume that all the balls are equally likely to be selected on a random draw from the bucket.

A) The probability that a randomly selected ping pong ball is dented =

B) Suppose that a randomly selected ball drawn from the bucket is dented. Given that the ball is dented, then the probability that its color is green =

A basket ball moving to the right at a speed of 10 m/s makes a head-on collision with a ping-pong ball moving to the left at 15 m/s. What will be the speed of the ping-pong ball after the collision. Ignore the air resistance.