There are 7 people taking part in a raffle.Ann, Elsa, Hans, Jim, Lena, Omar, and Soo.Suppose that prize winners are randomly selected from the 7 people.Compute the probability of each of the following events.Event A: Elsa is the first prize winner, Soo is second, Ann is third, and Lena is fourth.Event B: The first four prize winners are Soo, Jim, Elsa, and Lena, regardless of order.Write your answers as fractions in simplest form.
Question
There are 7 people taking part in a raffle.Ann, Elsa, Hans, Jim, Lena, Omar, and Soo.Suppose that prize winners are randomly selected from the 7 people.Compute the probability of each of the following events.Event A: Elsa is the first prize winner, Soo is second, Ann is third, and Lena is fourth.Event B: The first four prize winners are Soo, Jim, Elsa, and Lena, regardless of order.Write your answers as fractions in simplest form.
Solution
Event A:
The probability of Elsa being the first prize winner is 1/7, because there are 7 people and she is one of them.
After Elsa wins, there are 6 people left. The probability of Soo being the second prize winner is 1/6.
After Soo wins, there are 5 people left. The probability of Ann being the third prize winner is 1/5.
After Ann wins, there are 4 people left. The probability of Lena being the fourth prize winner is 1/4.
So, the probability of event A is the product of these probabilities, which is (1/7) * (1/6) * (1/5) * (1/4) = 1/840.
Event B:
The first four prize winners are Soo, Jim, Elsa, and Lena, regardless of order. This means we are looking at the number of ways to arrange 4 people out of 7, which is a combination.
The number of ways to choose 4 people out of 7 is 7 choose 4, which is 7! / (4!(7-4)!) = 35.
Each of these 35 groups of 4 people can be arranged in 4! = 24 ways.
So, there are 35 * 24 = 840 possible outcomes where Soo, Jim, Elsa, and Lena are the first four prize winners, regardless of order.
Since there are 7! = 5040 total possible outcomes, the probability of event B is 840/5040 = 1/6.
Similar Questions
A science class has 5 girls and 5 boys in the seventh grade and 3 girls and 1 boy in the eighth grade. The teacher randomly selects a seventh grader and an eighth grader from the class for a competition. What is the probability that the students she selects are both boys?Write your answer as a fraction in simplest form.
Of 162 students honored at an academic awards banquet, 48 won awards for mathematics and 78 won awards for English. There are 14 students who won awards for both mathematics and English. A student is selected at random for an interview. What is the probability that the student won an award for English or mathematics? Express your first answer as a fraction in simplest form. Round your percent answer to the nearest tenth. The probability that the student interviewed won an award for English or mathematics is , or about $\%$% .
(c) A prize wheel has 8 fields of different sizes that are numbered 1, 2, 3, 4, 5, 6, 7 and 8. The probabilities for the following events are known: 𝑃({8,1,3,7})=913 and 𝑃({8,2,4,5,6})=713.Find 𝑃({8})=? (Enter as a reduced fraction).
At a game show, there are 8 people (including you and your friend) in the front row.The host randomly chooses 3 people from the front row to be contestants.The order in which they are chosen does not matter.There are 8C3 = 56 total ways to choose the 3 contestants.What is the probability that you and your friend are both chosen?A.B.C.D.
Ryan has bought tickets for a raffle. The probability of his winning is 16. What are the odds in favor of his winning?:
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.