optional scarf? 2. Refer to Example 3.1.3 on page 80. María has just added a few more items to her wardrobe: 4 pairs of slacks, 2 turtlenecks, and a second jacket. Assume an outfit consists of a pair of shoes, a lower wear (either a skirt or a pair of slacks), an upper wear (a blouse, a turtleneck, or a combination of blouse and turtleneck), and an optional jacket. a) How many outfits ca María assemble with her new wardrobe? b) If the second jacket doesn't match well with one pair of shoes, and that is the only mismatch, how many well-matched outfits can María assemble with her new wardrobe? 3. a) How many 7-digit numbers are there? b) How many 7-digit numbers have no repeated digits? c) How many 7-digit numbers are a palindrome6? d) How many 7-digit palindrome numbers have no repeated digits? 4. Reconsider Example 3.1.9 from page 84, and break it into disjoint cases, so that the sum principle can be applied. 5. The Debate Club is holding elections for president and secretary. There are 5 candidates, 3 women and 2 men. The club bylaws require that both officers be of opposite gender. After ranking, the top candidate will be president and the top candidate of the opposite gender will
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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