An organization in Texas organizes lucky draw this month. 1 thousand tickets are sold for 4$ each. Each has an equal chance of winning. 2 tickets will win 267$, 8 tickets will win 163$ and 13 tickets will win 40$. Let, the random variable 𝑋X denote the net gain from purchase of one ticket. What is the probability that 𝑋X takes the value less than 163? (Enter the answer correct to 4 decimal place)
Question
An organization in Texas organizes lucky draw this month. 1 thousand tickets are sold for 4, 8 tickets will win 163. Let, the random variable 𝑋X denote the net gain from purchase of one ticket. What is the probability that 𝑋X takes the value less than 163? (Enter the answer correct to 4 decimal place)
Solution
To solve this problem, we first need to understand what the random variable X represents. X is the net gain from the purchase of one ticket. This means that X can take on the values of -4 (the cost of the ticket), 263 (267 - 4, the net gain if you win the 163 prize), and 36 (40 - 4, the net gain if you win the $40 prize).
The question asks for the probability that X takes the value less than 163. This means we are looking for the probability that X equals -4, 36, or 159.
The probability that X equals -4 is the probability that you do not win a prize. There are 1,000 tickets sold and 23 prizes (2 + 8 + 13), so there are 977 tickets that do not win a prize. Therefore, the probability that X equals -4 is 977/1000 = 0.977.
The probability that X equals 36 is the probability that you win the $40 prize. There are 13 tickets that win this prize, so the probability that X equals 36 is 13/1000 = 0.013.
The probability that X equals 159 is the probability that you win the $163 prize. There are 8 tickets that win this prize, so the probability that X equals 159 is 8/1000 = 0.008.
Therefore, the probability that X takes the value less than 163 is the sum of these probabilities: 0.977 + 0.013 + 0.008 = 0.998.
So, the probability that 𝑋X takes the value less than 163 is 0.9980.
Similar Questions
Ryan has bought tickets for a raffle. The probability of his winning is 16. What are the odds in favor of his winning?:
The winners of a carnival game draw a ticket from a box to determine their prize. Each winner draws a ticket and places it back into the box before the next draw. Every winner has a 28% chance of getting a pencil pouch, a 56% chance of getting a backpack, and a 16% chance of getting a gumball.The game operator wants to simulate what could happen for the next ten winners.So for each winner, she generates a random whole number from 1 to 100.She lets 1 to 28 represent a winner getting a pencil pouch, 29 to 84 a backpack, and 85 to 100 a gumball.Here is the game operator's simulation.Winner 1 2 3 4 5 6 7 8 9 10Random number 46 71 66 72 32 55 7 59 4 28In the simulation, which prize did each winner get?(a) Winner 4: (b) Winner 9: (c) Winner 10:
At a raffle, 1500 tickets are sold at $2.00 each for four prizes of $500, $250, $150, and $75. You buy one ticket. What is the expected value of your gain?X $498 $248 $148 $73 -$2P(X) 1/1500 1/1500 1/1500 1/1500 1496/1500Group of answer choices$193$1.35-$193-$1.35
A lottery contains eight prizes and twenty blanks. If a lottery is randomly drawn, then what is the probability of getting a prize?1/82/52/71/5
The net profit from a certain investment is normally distributed with a mean of \$2,500 and a standard deviation of \$1,000. The probability that the investor’s net gain will be at least \$2,000 is?Select one:a.0.0000.b.0.3413.c.0.0005.d.0.0500.e.0.5000.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.