An urn contains 8 red balls and 3 green balls. If Tim chooses 6 balls at random from the urn, what is the probability that he will select 4 red balls and 2 green balls? Round your answer to 3 decimal places. (If necessary, consult a list of formulas.)
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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O PROBABILITY
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Probabilities of draws without.
QUESTION
A history class is comprised of 4 female and 10 male students. If
instructor of the class randomly chooses 12 students from the cla
an oral exam, what is the probability that 3 female students and
students will be selected? Round your answer to 3 decimal place
(If necessary, consult a list of formulas.)
O EXPLANATION
We first count the number of different sets of 12 students that ca
selected from a class of 4+ 10=14 students. This is the number of
combinations of 14 items taken 12 at a time, which is equal to the
following.
14!
14C12-
= 91
12!2!
Other notations
The 91 different sets of 12 students can be considered as a sampl
Notice that each of the 91 sets of students in the sample space is
likely to be selected.
We next count the number of sets of students in the sample spa
have 3 female students and 9 male students. There are c, ways
the set of 3 female students from a class containing 4 female stu
and there are „C, ways to select the set of 9 male students from
containing 10 male students. Using the multiplication principle, we find the
of ways to select 3 female and 9 male students.
4!
„Cy'10C9= 311! 9!1!
10!
= 4-10-40
Therefore, we get the following.
P(instructor selects 3 female and 9 male students)
40
=0.44
91
ANSWER
0.44
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Probabilities of draws without...
An urn contains 8 red balls and 3 green balls. If Tim chooses 6 balls at
random from the urn, what is the probability that he will select 4 red
balls and 2 green balls? Round your answer to 3 decimal places.
(If necessary, consult a list of formulas.)
Explanation
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