Probability 1
What is the probability of drawing a red card in a standard deck of 52 cards?
26/52 = ½ = 0.5
20 What is the probability of rolling an even number with a 6-sided die numbered one through six?
3/6 = ½ = 0.5
If you randomly select a letter from the word "PROBABILITY", what is the probability that it is a vowel?
4/11 or 0.364
Measures the likelihood that an event will occur
Probability
What is the range of a probability?
0-1
If you were to roll the pair of dice, what is the probability that you will roll a 4 and a 2?
1/36
If you randomly select a card from a standard deck of 52 cards, what is the probability of selecting a face card (jack, queen, or king)?
12/52
In a class of 30 students, 18 are male and 12 are female. If a student is randomly selected, what is the probability of selecting a female student?
12/30 = 2/5 or 0.4
Types of events
Mutually exclusive
independent
Probability theory is the basis for ______.
Inferential statistics
A box contains 4 red marbles, 3 blue marbles, and 5 green marbles. What is the probability of drawing a blue marble?
3/12 = ¼ or 0.25
If you randomly select a month of the year, what is the probability of selecting a month with 31 days?
7/12 or 0.5833
You were given 100 marbles in 5 colors (red, yellow, green, blue, black). Each color has an equal number of marbles.
Sampling with replacement (put back in the bag after pulling the marble out) and drawing 2 from the bag of marbles, what probability would you choose red on either draw?
(20/100) + (20/100) = 0.4 or 2/5
Probability that an event will occur given that another event has already occurred
Conditional Probability
Provide 2 characteristics of a mutually exclusive event.
1. event cannot occur together
2. events do not have any common outcomes
Flip two coins and find the probabilities of the events:
Let G = the event of getting two faces (head-head, tail-tail) that are the same.
P(G) = 2/4
Let event C = taking an English class.
Let event D = taking a speech class.
Suppose P(C) = 0.75, P(D) = 0.3, P(C|D) = 0.75 and P(C AND D) = 0.225.
Justify your answers to the following questions numerically.
a. Yes, because P(C|D) = P(C)
b. No, because P(C and D) is not equal to zero.
Klaus is trying to choose where to go on vacation. His two choices are: A = New Zealand and B = Alaska.
Klaus can only afford one vacation. The probability that he chooses A is P(A) = 0.6 and the probability that he chooses B is P(B) = 0.35. What is the probability that he does not choose to go anywhere for his vacation?
P (A or B) = P(A) + P(B) = 0.6 + 0.35 = 0.95
1 – 0.95 = 0.05 not choosing anywhere for his vacation
Define independent events
occurrence of one event does not change the probability of the occurrence of the other event
Define dependent events
occurrence of one event affects the probability of the occurrence of another event
Flip two coins and find the probabilities of the events:
½ * 1 = ½
Note: 1 is independent from the first flip
Getting all tails occurs when tails show up on both coins (TT). H’s outcomes are HH and HT. J and H have nothing in common, so P(J and H) = 0. J and H are mutually exclusive.
Let event C = taking an English class. Let event D = taking a speech class.
Suppose P(C) = 0.75, P(D) = 0.3, P(C|D) = 0.75 and P(C AND D) = 0.225.
Justify your answers to the following questions numerically.
P(D|C) = P(C and D)/P(C) = 0.225/0.75 = 0.3
Studies show that about one woman in seven (approximately 14.3%) who live to be 90 will develop breast cancer. Suppose that of those women who develop breast cancer, a test is negative 2% of the time. Also suppose that in the general population of women, the test for breast cancer is negative about 85% of the time. Let B = woman develops breast cancer and let N = tests negative. Suppose one woman is selected at random.
P(B) = 0.143; P(N) = 0.85
Can two events be either mutually exclusive or independent?
YES! but only when event is not equal to zero.
Rules:
Mutually exclusive events always dependent.
Independent are never mutually exclusive.
Multiplication Rule - used to calculate probability of both independent events are going to happen
Addition Rule - used the probability that either one of the events is going to happen