Bernoulli 2 Do these situations involve Bernoulli trials?Explain.a) You are rolling 5 dice and need to get at least two 6’sto win the game.b) We record the distribution of eye colors found in agroup of 500 people.c) A manufacturer recalls a doll because about 3% havebuttons that are not properly attached. Customersreturn 37 of these dolls to the local toy store. Is themanufacturer likely to find any dangerous buttons?d) A city council of 11 Republicans and 8 Democrats picks a committee of 4 at random. What’s the prob-ability they choose all Democrats? e) A 2002 Rutgers University study found that 74% ofhigh school students have cheated on a test at leastonce. Your local high school principal conducts asurvey in homerooms and gets responses that admitto cheating from 322 of the 481 students.
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.
Explain.
a) You are rolling 5 dice and need to get at least two 6’s
to win the game.
b) We record the distribution of eye colors found in a
group of 500 people.
c) A manufacturer recalls a doll because about 3% have
buttons that are not properly attached. Customers
return 37 of these dolls to the local toy store. Is the
manufacturer likely to find any dangerous buttons?
d) A city council of 11 Republicans and 8 Democrats
ability they choose all Democrats?
high school students have cheated on a test at least
once. Your local high school principal conducts a
survey in homerooms and gets responses that admit
to cheating from 322 of the 481 students.
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