Basic Probabilities
What is the probability of rolling a standard die and getting a 7?
0
(dice have 1-6 only)
A cup has sticks numbered 1 through 13. What are the odds in favor of drawing an odd number?
7/6
(7 odds and 6 evens in 1-13 ... odds = good / bad)
A & B are disjoint
P(A) = 0.37 and P(B) = 0.63
Find P(A or B)
1
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P(A or B) = P(A) + P(B)
= 0.37 + 0.63
A coin is tossed and then a die is rolled. What is the probability of getting a heads and then an even number?
(1/2 * 1/2 =) 1/4
What is experimental probability?
When probabilities are found using the data from an experiment.
Given a bag of marbles containing 15 yellow, 12 blue and 8 green, what is the probability of drawing a yellow marble?
15/35 = 3/7
A spinner has 6 equal sections, red, blue, yellow, green, orange, and pink. What are the odds of landing on the orange section?
1/5
If P(A) = 8/15, P(A or B) = 3/5 and P(A and B) = 2/15 then what is P(B)?
1/5
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P(A or B) = P(A) + P(B) - P(A and B)
3/5 = 8/15 + P(B) - 2/15
3/5 = 6/15 + P(B)
3/5 = 2/5 + P(B)
1/5 = P(B)
A bag contains the following marbles: 4 red, 2 green, 3 yellow, and 1 orange. What is the probability that a green then a red will be picked, if the marble is replaced for the second draw.
2/25
(2/10 * 4/10) = 8/100 = 2/25)
A boy tosses a coin and gets heads 7 times out of 20. Is this theoretical or experimental?
Experimental
What is the probability of drawing a heart from a standard deck of cards?
13/52 = 1/4
A spinner has 10 equal sections, 1,2,3,4,5,6,7,8,9, and 10. If the spinner is spun, what are the odds against getting a number less than 7?
1/2
[bad/good = (7,8,9)/(1,2,3,4,5,6) = 3/6 = 1/2]
Out of a standard deck of cards what is the probability of drawing a red card or a queen?
7/13
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P(R or Q) = P(R) + P(Q) - P(R and Q)
= 26/52 + 4/52 - 2/52
= 28/52
A spinner is divided into 10 equal regions numbered 1 to 10.
What is the probability that you will perfect squares 3 times in a row?
0.027
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{Perfect Squares = 1, 4, 9}
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P(PS and PS and PS) = (3/10)*(3/10)*(3/10)
= 27/1000
The probability of drawing a face card from a standard deck of cards is 3/13. Is this theoretical or experimental probability?
Theoretical
Given the numbers 0 through 20, what is the probability of choosing an odd number?
10/21
A drawer contains 20 socks: 8 blue, 4 green, 6 black, and 2 white. What are the odds of picking a sock whose color begins with b?
7/3
(good/bad = blue+black/green+white = 14/6 = 7/3)
If event A is rolling a standard 6 sided die and event B is choosing an even number between 1 and 10 are the events disjoint or overlapping?
Overlapping - both events have the numbers 2, 4 and 6.
A drawer contains 4 white, 4 black, 2 yellow, and 5 polka-dot socks and the shoe rack has 2 pairs of black shoes, a pair of blue shoes 1 pair of tennis shoes and 3 pairs of brown shoes.
What is the probability that Julie will choose a pair of polka-dot socks and blue shoes to wear to school?
approx. 0.04762
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P(polka and blue) = P(polka) * P(blue)
= (5/15) * (1/7)
= (1/3) * (1/7)
= 1/21
A heart is randomly chosen from a deck of cards 7 out of 12 times. What is the experimental probability?
7/12
Given the numbers 1 through 15, what is the probability that a factor of 20 is chosen?
Factors of 20: 1 & 20, 2 & 10, 4 & 5
We only have 1-15 so the 20 is removed from the count.
5/15 = 1/3
A class 32 students and 12 of them are girls. What are the odds against the teacher choosing a girl?
5/3
(bad/good = boys/girls = 20/12 = 5/3)
A class fundraiser sells 175 raffle tickets for an Amazon gift card and 200 raffle tickets for set of 15 movie tickets. You buy 10 tickets for each raffle.
What is the probability that you will win one of the raffles?
approx. 0.10714
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P(Amazon or movies) = P(Amazon) + P(movies) - P(Amazon and movies)
= (10/175) + (10/200) - 0
= (2/35) + (1/20)
= 3/28
At a specific manufacturing plant it has been found that 4 out of every 300 widgets is defective. What is the probability of choosing at least one defective widget out of the first 50?
approximately 0.48888
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P(def) = 4/300
P(not def) = 296/300
P(def >= 1) = 1 - P(no def)50
= 1- (296/300)50
A heart is randomly chosen from a deck of cards 7 out of 12 times. What is the theoretical probability?
1/4
[It asked about the THEORETICAL probability (13 hearts out of 52 cards) not the experimental probability!]