In a state's Pick 3 lottery game, you pay $1.35 to select a sequence of three digits (from 0 to 9), such as 155. If you select the same sequence of three digits that are drawn, you win and collect $441.25. Complete parts (a) through (e). a. How many different selections are possible? b. What is the probability of winning? | Type an integer or a decimal.) c. If you win, what is your net profit? $ (Type an integer or a decimal.) d. Find the expected value. | (Round to the nearest hundredth as needed.) e. If you bet $1.35 in a certain state's Pick 4 game, the expected value is - $0.91. Which bet is better, a $1.35 bet in the Pick 3 game or a $1.35 bet in the Pick 4 game? Explain. Click to select your answer(s).
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Part a:
For a three digit number the first number can be any number from 0 to 9. Thus, there will be 10 possible ways of selecting first number. Similarly for the second and third number there will be 10 possible ways of selecting the second and third number.
Thus, the different selections that are possible is 10 × 10 × 10 = 1000.
Part b:
The probability of winning is 1/1000 = 0.001.
Part c:
If we win the net profit will be,
Net profit = $-1.35 + $441.25 = $439.9.
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