Let X denote the number of times you have to play a game in order to win once. Assume attempts are independent, and that the chance of winning each time you play is p.
(a) Find the probability that X is even (as a function of p). [Hint: You’ll use a geometric series from calculus.]
(b) What happens to your answer to (a) as p → 1?
Let X denote the number of times you have to play a game in order to...
In a certain game of chance, your chances of winning are 0.2 on each play. If you play the game five times and outcomes of each play are independent, the probability that you win at least once is (A) 0.6723 (B) 0.1091 (C) 0.2000 (D) 0.3277 the answer is A but how is it A
Problem: A game gives you the probability .10 of winning on any 1 play. Plays are independent of each other. You play a total of 4 times. Let X represent the number of times you win. a) What is the probability that you don't win at all? b) what is the probability that you win at least once? c) what is the probability that you win once or twice? d) what is the expected value of X? What is the...
An instant lottery game gives you probability 0.10 of winning on any one play. Plays are independent of each other. You play 4 times. a) If X is the number of times you win, contract the probability distribution of X. b) What is the probability that you don't win at all? c) What is the probability that you win at least once? d) What is the expected value of X? What is the standard deviation of X?
Your probability of winning a game of chance is 0.4. If you play the game 3 times, what is the probability that you will win exactly 2 times?
3. In a certain game of chance, you have a 3/4 chance of winning each time you play (with the outcomes each time you play independent of each other). Suppose you play the game until you win for the first time. What is the probability you will win the game on the first, second, or third time playing it?
3. In a certain game of chance, you have a 3/4 chance of winning each time you play with the outcomes each time you play independent of each other). Suppose you play the game until you win for the first time. What is the probability you will win the game on the first second, or third time playing it? 4. A box of 40 fuses contains 10 fuses which are defective. If you randomly choose a collection of 5 fuses...
You play two games against the same opponent. The probability you win the first game is 0.8. If you win the first game, the probability you also win the second is 0.6. If you lose the first game, the probability that you win the second is 0.4. Complete parts a) through e). a) Are the two games independent? Explain your answer A. Yes; all events are independent. O B. No; the outcome of the first game determines the probability of...
The probability you win a game is 0.40. If you play the game 90 times, what is the most likely number of wins you will get? This is the same is the mean of the binomial distribution with N=90 and p=0.40, and it is also the expected value of playing the game 90 times.
We play a game where we throw a coin at most 4 times. If we get 2 heads at any point, then we win the game. If we do not get 2 heads after 4 tosses, then we loose the game. For example, HT H, is a winning case, while T HT T is a losing one. We define an indicator random variable X as the win from this game. (d) (5 Pts.) On average how many times do you...
An instant lottery game gives you probability 0.02 of winning on any one play. Plays are independent of each other. If you play 7 times What P(winning none of your plays)? What is the P(winning at least 2 or more plays)?