In a famous study done in the 1960s two dolphins, Doris and Buzz, were trained to work together to earn fish. Doris was shown a light underwater. If the light was on steadily, her partner Buzz on the other side of the tank needed to press a button on the right for them to earn fish. If the light was blinking, he needed to press a button on the left. At one point in the study, the researcher hung a canvas in the middle of the tank in such a way that Buzz could not see the light. After looking at the light, Doris “swam near the curtain and began to whistle loudly. Shortly after that Buzz whistled back and then pressed the correct button". (Tintle, Rossman and Chance, MAA Prep Workshop) Of course, getting it right once was not enough to convince the scientists that there was really communication going on. It turned out, that in 15 out of 16 trials the dolphin pushed the correct button. Of course, it is possible that this happened just out of random chance - that the second dolphin just happened to hit a lucky streak. We want to try to determine just how unlikely that would be. 5. Using a significance level of 0.05, test the claim that the dolphins were communicating with each other that led them to choose the correct button more than 50% of the time. Using your calculator, and the test statistic and information you found in the last question, find the p-value.
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.
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