1. Suppose that a sample space consists of n equally likely outcomes. Select all
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Question
1. Suppose that a sample space consists of n equally likely outcomes.
Select all of the statements that must be true.
Any two events in the sample space have equal probablity of occurring.
The probability of any event occurring is the number of ways the event can occur divided by n.
The probability of any one outcome occurring is 1n.
Probabilities can be assigned to outcomes in any manner as long as the sum of probabilities of all outcomes in the sample space is 1.
2. Select all of the statements that are axioms of probability.
The probability of two events occurring is always greater than 0.
If two events A and B are mutually exclusive (disjoint), then P(A or B)=P(A)+P(B).
The combined probability of all possible outcomes is equal to 1.
The probability of an event is a number that is at least 0 and no more than 1.
The probability of an event A is the number of outcomes in A divided by the number of outcomes in the sample space.
3. Jim owns a vehicle. Select all of the mutually exclusive events from the following events.
Jim's vehicle is a tractor.
Jim's vehicle has a broken headlight.
Jim's vehicle is a recreational vehicle (RV).
Jim's vehicle is black.
Jim's vehicle is a sport utility vehicle (SUV).
4.
The prizes at a carnival tossing game are different stuffed animals. There are 34 tigers, 27 bears, 12 hippopotamuses, 16 giraffes, and 22 monkeys. The carnival manager randomly selects a prize when a player wins the game.
Determine the probability that the prize selected is not a hippopotamus. Give your answer as a decimal, precise to three decimal places.
5.
You and a group of friends are going to a five-day outdoor music festival during spring break. You hope it does not rain during the festival, but the weather forecast says there is a 45% chance of rain on the first day, a 55% chance of rain on the second day, a 10% chance of rain on the third day, a 10% chance of rain on the fourth day, and a 5% chance of rain on the fifth day.
Assume these probabilities are independent of whether it rained on the previous day or not. What is the probability that it does not rain during the entire festival? Express your answer as a percentage to two decimal places.
6.
Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to get to work on time. If he leaves now and does not get stopped by any traffic lights, he will arrive at work in exactly 8 minutes. In between his house and his work there are three traffic lights, A, B, and C. Each light that stops him will cause him to arrive an additional 2 minutes later. The following table displays the probability that he is stopped by each of the three traffic lights. Assume that the probability that he is stopped by any given light is independent of the probability that he is stopped by any other light.
What is the probability that the employee is not late for work? Please write your answer in decimal form, rounded to three decimal places.
P(employee is not late for work)= ???
Traffic light A Traffic light B Traffic light C P(A) P(B) P(C) 0.4 0.8 0.3Explanation / Answer
1. Here sample space have n equally likely outcomes, so equal probability
Now as we know P(x) is ratio of the number ofoutcomes favourable to total number
Based on above things
Any two events in the sample space have equal probablity of occurring.
The probability of any event occurring is the number of ways the event can occur divided by n.
Probabilities can be assigned to outcomes in any manner as long as the sum of probabilities of all outcomes in the sample space is 1.
Are correct statements
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