You set up a camival booth game at a local fund-raising event. The game consists of rolling a giant six-sided die. The die is fair, so each individual roll has a probability of %. Game participants pay $3 per roll. A participant who rolls a 6 wins a prize that costs you $8. A participant who rolls a1 wins a prize that costs you $2.50. Participants who roll other numbers win nothing. Think about the expected earnings the booth owner will receive for each person who plays the game. Roll 6. 1 2,3,4, or 5 Earnings Probability a. What is the expected value or mean for each participant? b. An average of 35 participants play your game each hour, and the event lasts 8 hours. How much money do you expect to raise during the event? O. sa
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
If a die is rolled then getting 2, 3, 4 and 5 are mutually exclusive events. So the probability of getting 2, 3, 4 or 5 can be computed by adding the probability of each individual event. The probability of each individual roll is .
Now, the participant gives $3 and if participant roll 6, the winning price is worth of $8, so the earning will be . If participant roll 1 then winning price is worth of $2.50, so the earning will be . And rolling 2 or 3 or 4 or 5 will give nothing to the participant, so earning will be $3.
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