Two cards are chosen at random without replacement from the following set {T, T, E, E, E}. Let A be the event that the first card chosen is a “T” and let B be the event that the second card chosen is a ”T”. Which of the following is true: (a) A and B are both independent and mutually exclusive. (b) A and B are independent but not mutually exclusive.
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) Two cards are chosen at random without replacement from the following set {T, T, E, E, E}.
Let A be the
the second card chosen is a ”T”. Which of the following is true:
(a) A and B are both independent and mutually exclusive.
(b) A and B are independent but not mutually exclusive.
(c) A and B are mutually exclusive but not independent.
(d) A and B are neither mutually exclusive nor independent.
b) Which statement is correct about a p-value interpretation?
A) The smaller the p-value the stronger the evidence against the alternative hypothesis
B) smaller the p-value the stronger the evidence against the null hypothesis
C) larger the p-value the stronger the evidence against the alternative hypothesis
D) larger the p-value the stronger the evidence against the null hypothesis
E) None of the above
c) If a histogram is skewed to the right, then the mean is less than the
F
d) Which one of the following (mean/median) is the least sensitive to extreme values
in the data.
e) (A deck of cards has 52 cards, 26 red and 26 black.) Two cards are chosen from
a deck of cards sequentially without replacement. Let A be the event that the
first card is red. Let B be the event that the second card is black. Are A and B
independent? (YES or NO)
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