Theoretical vs Experimental
What is the difference between theoretical probability and experimental probability?
- Theoretical probability is the likelihood of an event happening based on mathematical reasoning.
- Experimental probability is the likelihood of an event happening based on experimental data or observations.
What is the general formula for calculating AND Events?
P(A ∩ B) = P(A) x P(B)
What is the general formula for calculating Inclusive OR events?
P(A U B) = P(A) + P(B) - P(A ∩ B)
What is the general formula for calculating Exclusive OR events?
P(A U B) = P(A) + P(B)
What is the general formula for the complementary events rule?
P(E) + P(E') = 1
A bag contains 6 red marbles and 4 blue marbles. What is the theoretical probability of randomly selecting a red marble?
The theoretical probability of selecting a red marble is 3/5. (6/10)
There are 2 Freddo frogs, 3 Caramello Koalas and 3 Flake bars. What is the chance of pulling out a Freddo frog and a Caramello Koala?
P(A ∩ B) = P(A) x P(B)
= 2/8 x 3/8
= 6/64
= 3/32
In a deck of cards, what is the probability of drawing either a red card or a face card?
P(A or B) = P(A) + P(B) - P(A ∩ B)
= 26/52 + 12/52 - 6/52
= 26/52 + 6/52
= 32/52
= 8/13
A bag contains 6 red marbles and 4 blue marbles. If you draw one marble at random, what is the probability of drawing a red marble or a blue marble?
P(A U B) = P(A) + P(B)
= 6/10 + 4/10
= 10/10
= 1
The probability of an event and its complement should always be what?
1 / 100% /exhaustive / mutually exclusive
In a game, a six-sided die is rolled 200 times, and the number 3 comes up 40 times. What is the experimental probability of rolling a 3?
1/5
(40/200)
You draw a card from a standard deck of 52 cards. What is the probability that it is a red card (hearts or diamonds) and a face card (jack, queen, or king)?
P(A ∩ B) = P(A) x P(B)
= 1/2 x 3/13
= 3/26
A jar contains 10 red, 5 blue, and 3 green marbles. If one marble is drawn at random, what is the probability of getting either a red marble or a blue marble?
P(A or B) = P(A) + P(B) - P(A ∩ B)
= 5/9 + 5/18
= 10/18 + 5/18
= 15/18
= 5/6
In a school orchestra 15 people play strings 10 play brass, 15 play woodwind, and 10 play percussion. If the conductor chooses a player at random to pick on, what is the probability that it will be a brass or woodwind player?
P(A U B) = P(A) + P(B)
= 10/50 + 15/50
= 25/50
= 1/2
Are "He will fall asleep by 11 pm" and "He will fall asleep by 10pm" complement events? Explain your answer
No because they are not exhaustive - they don't cover all options and won't = 1. The complement would be "He won't fall asleep by 11 pm"
When 60 light bulbs were tested, 3 were found to be faulty. In a carton of 600 such bulbs, how many you would expect to be faulty?
30
3/60 * 600 = 30
A bag contains 4 white, 5 black, and 3 red balls. Two balls are drawn at random without replacement. What is the probability that no black balls are drawn?
P(A ∩ B) = P(A) x P(B)
= 7/12 x 7/11
= 49/132
= 7/22
In a group of students, 60% like pizza and 40% like burgers. If 30% like both pizza and burgers, what is the probability that a student chosen at random likes either pizza or burgers?
P(A or B) = P(A) + P(B) - P(A ∩ B)
= 6/10 + 4/10 - 3/10
= 6/10 + 1/10
= 7/10
The canteen has 5 chocolate milks, 7 pies, 8 pasties, and 13 toasties. If the lunch lady gives you 2 items at random, what is the probability that you will get a chocolate milk and a pie.
P(A U B) = P(A) + P(B)
= 5/33 + 7/33
= 12/33
= 4/11
The probability we will win the game is 6/10 and the probability we will tie is 1/10. What is the probability we will lose?
P(E') = 1 - P(E)
P(E') = 1 - 7/10
P(E') = 3/10
A jar contains 100 marbles, 60 of which are green and 40 of which are blue. If a marble is selected at random 120 times, and a green marble is selected 70 times, what is the experimental probability of selecting a green marble?
7/12
(70/120)
I have a bag of 15 skittles. 5 red, 7 green, and 3 yellow. What is the probability that you will choose at random a green skittle and a yellow skittle, without replacement?
P(A ∩ B) = P(A) x P(B)
= 7/15 x 3/14
= 21/210
= 1/10
The conductor of a big band is choosing a new chart for everyone to play. What is the probability she will choose an upbeat song or a funk song.
There are 40 charts
23 are funk songs
16 are upbeat
8 are both upbeat and funk
P(A or B) = P(A) + P(B) - P(A ∩ B)
= 23/40 + 16/40 - 8/40
= 22/40 + 8/40
= 30/40
= 3/4
Over the past couple of days, Louis' Greyhound (Charlie) has gone to the toilet as follows: 5 x in the garden bed, 3 x in the pot plants, 8 x behind the shed, 15 x on the side of the house. What is the probability that he will go to the toilet on the side of the house or in the garden bed?
P(A U B) = P(A) + P(B)
= 15/31 + 5/31
= 20/31
What is the complementary event for rolling a 6 on a die, what is its probability and why?
Not rolling a 6
5/6
P(E) = 1/6
P(E') = 1 - 1/6
P(E') = 5/6