. There are three coins in a box. One is a two-headed coin, another is a fair coin, and the third is a biased coin that comes up tails 25 percent of the time. When one of the three coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin?
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.
1. There are three coins in a box. One is a two-headed coin, another is a fair coin, and the third
is a biased coin that comes up tails 25 percent of the time. When one of the three coins is
selected at random and flipped, it shows heads. What is the
two-headed coin?
2. A bag contains 20 balls numbered 1 through 20. Suppose, you are rolling two regular six-sided dice and two four-sided dice together. Let’s
say, the sum of the numbers appearing on the two regular six-sided dice is ‘A’ and the sum of
the numbers appearing on the two four-sided dice is ‘B’. What is the probability that the
product of A and B is 12?
3. A bag contains 20 balls numbered 1 through 30. Suppose drawing an even-numbered ball is
considered a ‘Success’.
a. Two balls are drawn from the bag with replacement. Find the probability of getting:
i. Two successes
ii. exactly one success
iii. at least one success
iv. no successes
b. Find the same four probabilities for the experiment where the two balls are
drawn without replacement.
4. Suppose, you are attending a test where there are 9 multiple choice questions with 3
options in each. A question can have multiple correct answers and in that case, you
have to tick all of the correct choices to get the question right.
a. What is the probability that you’ll get exactly 6 of the questions right?
b. What is the probability that you’ll get at most 6 of the questions right?
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