17. In a recent fictional survey, 88 people were asked which Back to the Future installments they liked. 55 people liked Back to the Future I, 16 people liked Back to the Future II, and 43 people liked Back to the Future III. There were 26 people that liked more than one of the movies. 13 people liked numbers l and II, 7 people liked numbers 11 and ill, and 16 people liked numbers l and Ш How many people didn't like any of the films? How many people liked only one of the films? How many people liked I or III? How many people liked II and III, but not I? How many people do not like Back to the Future II?
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.
For this question you need to use Combination, Permutation and Complement principal.
As per norms, the first three questions are answered. To find the number of element in various combinations of sets
The Venn diagram for the given word problem : Here A , B and C represent I, II and III (for simplifiying notation). From the given data, first find the number of elements common to all : that is number of elements in A and B and C , as shown.
Finding the number of elements common to all A , B and C=5
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