Independent & Dependent
You flip a coin and then roll a 6-sided dice. Is this event independent or dependent?
Independent
The coin flip does not affect the dice roll
You roll a standard 6-sided dice 60 times, and get a "6" fifteen times. What is the experimental probability of rolling a 6?
15/60 = 1/4 = .25 or 25%
True or False: Landing on Heads and landing on Tails with a single coin flip is a mutually exclusive event.
True: They cannot happen at the same time.
In a Venn Diagram of 100 seniors, 65 play sports, 40 are in clubs, and 20 are in both. How many students do neither?
Sports only 65-20 = 45
Clubs only 40-20 = 20
Both 20
45 + 20 + 20 = 85
100-85=15 do neither!
A coin lands on Heads 5 times in a row, what is the probability that the next flip will land on Heads?
50% or 1/2
You draw a card from a deck of cards, keep it, then draw another. Is this event independent or dependent?
Dependent
If you don't replace the card, it changes the total
What is the theoretical probability as a percentage of rolling a 3 on a 9-sided die?
1/9 = .11 or 11.11%
From a single deck of cards, is drawing a spade card and a Jack, mutually exclusive?
No, Spade Jacks exist, so they overlap.
On a probability tree diagram, Path A has a probability of 0.8 and Path B has a probability of 0.7. What is the P(Path A and Path B)?
0.8 * 0.7 = 0.56 or 56%
If the probability of an event occurring is 0.37, what is the probability of the event NOT occurring?
1-0.37 = 0.63 or 63%
A bag contains 3 red and 7 blue marbles. If you draw 2 marbles in a row without replacement, what is the probability that both are red?
6.66% or 1/15
A 9-sided die is rolled 100 times, resulting in sixteen 3's. Is 16% the theoretical or experimental probability?
Experimental Probability
Answer is based on the actual rolls.
On a single roll, what is the P(Rolling a 2 or a 5)?
P(A or B) = P(A) + P(B)
P(2) = 1/6
P(5) = 1/6
P(2 + 5) = 2/6 or 33.3%
In a 2-way table, 31 frequently ate burgers, 38 rarely ate burgers, 22 frequently ate hot dogs, 19 rarely ate hot dogs. How many people were surveyed?
31+38+22+19 = 110 people were surveyed.
A carnival game owner needs the win rate to be under 15%. If the win probability is calculated as 2/15, should they keep the game?
13.33% is less than 15%
If event A and Event B are independent, with P(A) = 0.4 and P(B) = 0.5, what is P(A and B?)
(0.4 * 0.5) = 0.20 or 20%
In a 100-page book, what is the theoretical probability of randomly opening to a page that is a multiple of 9?
11/100 or 11%
Pages: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
Events A and B are mutually exclusive. If P(A) = 0.35 and P(B) = 0.45, what is P(A or B)?
P(A) + P(B) = P(A or B)
0.35 + 0.45 = 0.80 or 80%
If 22 people frequently ate hot dogs out of 110 people surveyed, what percentage of people frequently eat hot dogs?
22/110 = 20%
In a room full of 180 graduates, 45 are STEM majors. What is the probability of choosing a non-stem graduate?
(180-45) / 180 = 135/180 = 0.75
A bag has 5 apple and 10 lime candies. If you pick one, eat it, and pick another. What is the probability that both candies picked are apple?
(5/15) * (4/14) = (20/210)
= .09 or 9%
A basketball coach only wants to start someone who can make at least 80% of their free-throws. If Big Bird makes 270 of his 300 attempts, can he start?
Specifically he makes 90%!
If P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.1, are events A and B mutually exclusive?
P(A or B) = P(A) + P(B) - P(A and B)
No because P(A and B) is not equal to 0. If P(A and B) is not zero, then there is a chance of both events happening at the same time (overlap)
Out of 200 test takers, 120 took a prep course (105 passed), and 80 did not take the prep course (45 passed). How many total students failed?
Prep course Fails = 120-105 = 15
No Prep Fails = 80-45 = 35
Total Failed = 15+35 = 50
Why cant you add just P(A) + P(B) to find P(A or B) when events overlap?
Because the overlapping outcome P(A and B) would be counted twice!