A box of cookies contains 2 chocolate and 8 butter cookies. Miguel randomly selects a cookie and eats it. Then he randomly selects another cookie and eats it. (How many cookies did he take?) a)Draw the tree that represents the possibilities for the cookie selections. Write the probabilities along each branch of the tree. (Let B be the event that he selected a butter cookie, and let C be the event that he selected a chocolate cookie. Enter your probabilities as fractions.) b)Are the probabilities for the flavor of the second cookie that Miguel selects independent of his first selection? Explain. c)For each complete path through the tree, write the event it represents and find the probabilities. (Enter your probabilities as fractions.) P(BB) = P(BC) = P(CB) = P(CC) =
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.
A box of cookies contains 2 chocolate and 8 butter cookies. Miguel randomly selects a cookie and eats it. Then he randomly selects another cookie and eats it. (How many cookies did he take?)
a)Draw the tree that represents the possibilities for the cookie selections. Write the probabilities along each branch of the tree. (Let B be the
| P(BB) | = | |
| P(BC) | = | |
| P(CB) | = | |
| P(CC) | = |
d)Let S be the event that both cookies selected were the same flavor. Find P(S). (Enter your
e.Let T be the event that both cookies selected were different flavors. Find P(T) by two different methods: by using the complement rule and by using the branches of the tree. Your answers should be the same with both methods. (Enter your probability as a fraction.)
f.Let U be the event that the second cookie selected is a butter cookie. Find P(U). (Enter your probability as a fraction.)
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