the discussion below by classifying

Review and respond to the discussion below by classifying the examples and providing a reason. Check the replies to see if they are accurate. 1. An independent event is an event that is not affected by prior events but a dependent event is one that is affected by prior events. For example, If you work hard to go above and beyond in your job every day and then you get a promotion. This would be considered a dependent event because you most likely would not have gotten the promotion if you didn’t go above and beyond for it. Which means that the probability of getting a promotion depends on how hard you work. Example 1: You have entered your name into a raffle with six tickets and thirty-two people entered their name. Every time they call a name they put the ticket back in the hat. What is the possibility that your name will be called next? Example 2: You have entered your name into a raffle with six tickets and thirty-two people entered their name. Every time they call a name they pull the ticket out of the hat and place it aside. What is the possibility that your name will be called next? 2. An independent event, when referring to statistics, is an event that does not rely on any outside factors. The example of a coin flip has been used ad nauseam because it is a perfect example of an independent event. Here is my attempt at an example: Joe Kicksalot can successfully kick a 35-yard field goal 75% of the time. Each time Joe kicks a 35-yard field goal is a singular event. Each time he kicks it, he has a , a 0.75, or a 75% chance to make it. This singular event would be considered independent. Now lets make this a little more interesting. Lets see the probability of him making 3 in-a-row. Each event is dependent on the previous since he must make all three in order to satisfy the requirement. Heres what it would look like: P(of Joe making 3 in-a-row or M) = P(M1 * M2 * M3) = P(M)3 So, this may seem a little complicated at first, however, all we must do is multiply each event with the next. If you looked at a million Joes, on their first attempt, 75% of them would have made the kick. Of that 75%, 75% of them would make the second kick. Again, of the Joes that made the second kick, 75% of them would make the third kick. Sounds a bit confusing? Heres what it looks like mathematically: P(0.75 * 0.75 * 0.75) or P(0.75)3 = 0.421875 = 42.2% Another example of a dependent event could be using a randomizer to pick a workout-of-the-day from a pool of 14 workouts labeled A N. That workout gets pulled out of the pool for the next day. Each day you will have one less workout. The chances that workout C will be picked at least on one of the first 3 days would look something like this: P(Day 1 Workout) = 1/14 = 7% Chance This also means that there is a 93% chance that it is not picked. P(Day 2 Workout|P(C is Not Picked)) = 1/13 = 8% Chance Again, 92% chance it isnt picked. P(Day 3 Workout|P(C is Not Picked)) = 1/12 = 8.3% Chance 91.7% not picked Of the three days, the probability would be determined by finding the sum of all the days: 1/14 + 1/13 + 1/12 = 253/1092 = 0.23168498 = 23% Using these methods, can you find some statistics for the game of Blackjack? Or maybe a probability statistic based on spinning a wheel with 12 possible prizes. Please make sure you provide some feedback. I appreciate constructive criticism.

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