If you play roulettes and bet on 'red' the probability that you win is 18/38 = .4737. People often repeat this between several times. We can consider each time we play a 'trial' and consider it a success when we win, so p = 18/38 or (.4737) and q = 20/38 or (.5263). Suppose that Caryl always places the same bet when she plays roulette, $5 on 'red'. Caryl might play just once, or might play several times. She has a profit (having won $5 more times than she lost $5) if she wins more than half of the games she plays. -when you play 401 times, p is the proportion of those 401 games that you win. You'll profit (winning more than you lose) if you win more than half of your bets p > .5000. e) assume that the distribution of p is Normal and find the probability that Caryl will have a profit if she plays 401 times. show your work or calculator input and round your answer to four decimal places f) twenty years ago, we didnt have the computing power in our hands to easily find the answer to part e) treating this as a binominal, but now your calulator can quickly do the calculations for you. Show your calulator input and answer (to four decimal places) as your binomcdf (to find the probability that Caryl profits when playing 401 times)
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.
If you play roulettes and bet on 'red' the
Suppose that Caryl always places the same bet when she plays roulette, $5 on 'red'. Caryl might play just once, or might play several times. She has a profit (having won $5 more times than she lost $5) if she wins more than half of the games she plays.
-when you play 401 times, p is the proportion of those 401 games that you win. You'll profit (winning more than you lose) if you win more than half of your bets p > .5000.
e) assume that the distribution of p is Normal and find the probability that Caryl will have a profit if she plays 401 times. show your work or calculator input and round your answer to four decimal places
f) twenty years ago, we didnt have the computing power in our hands to easily find the answer to part e) treating this as a binominal, but now your calulator can quickly do the calculations for you. Show your calulator input and answer (to four decimal places) as your binomcdf (to find the probability that Caryl profits when playing 401 times)
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