Probability Practice Problems
What is the probability of a fair coin landing heads on the tenth time it is flipped?
50% or .5, the probability of flipping a coin landing heads never changes no matter how many times u flip it as their are only 2 possible out comes and only 1 desired outcome [P(A)= Outcomes of A/total oucomes]
If the probability of a NASCAR racer making it through the race without a crash is .8 and the probability of a frog living to old age is .15, what is the probability that one of these events occurs?
As these two events are disjoint, the probability that one or the other occurs is the sum of their probabilities [P(AUB)= P(A) + P(B)], thus the probability of one of these events happening is .8 +.15, which is .95
If the probability of a dictator starting a genocide is .99, and the probability of the UN dismantling his dictatorship is .001, what is the probability of both events occuring
The probability of both events is found by multiplying the individual probabilities together [P(AΩB)=P(A) x P(B)], thus we find the probability of the dictator comiting genocide and being kicked out of power is .99 x .001 which equals .00099
If the probability that the president doesn't declare war is .98, then what is the probability that the president does declare war?
As P(A)= 1-P(A^C) [P(A^C) is the probability that P(A) doesn't happen] the probability that the president doesn't declare war is 1-.98 which is .02
What is the probability that a fair, six sided die rolls a 6?
As P(A)= Outcomes of A/total outcomes, the probability that a six sided die rolls a 6 is 1/6 or .166667
In the same scenario as the last card, what is the probability that both events occur?
As these events are independent, the probability that they both occur is the product of their probabilities [P(AΩB)=P(A) x P(B)], thus the probability of both evens occuring is .8 x .15 which is .12
What is the probability that both an engine fails on a plane and the plane crashes if the probability on an engine failure is .2, the probability of a plane crash is .1, and the probability of both is .02, what is the probability of one of these events occurring?
These events are not exclusive, which means we must use the general addition rule which states that in order to add the probabilities of non-exclusive events one mus add together the probabilities of each event and then subtract the probability of both events occurring together [P(AUB)= P(A) + P(B) - P(AΩB)]. Thus, the probability of either the plane crashing or the engine failing is .2 + .1 - .02, which equals .28
If a school of 400 has 150 girl students and 256 athletes (of which 100 are girls), what is the probability that a student is a girl given that they are an athlete?
To find probabilities in conditional distributions we must simply divide the probability of both events happening by the probability of the given probability [P(B|A)= P(AΩB)/P(A)], thus the probability that a student is female given that the student is an athlete is (100/400)/(256/400) which equals .390625 or 39.0523%
If the probability of getting turkey is .3 and the probability of getting ham is .4, what is the probability of getting turkey or ham if the probability of getting both is .12
We use the equation [P(AUB)= P(A) + P(B) - P(AΩB)] to find that the probability of getting either turkey or ham is .3 + .4 - .12 which equals .58
The probability of a car being a ford is .34 and the probability of a car being a ford given that it has good tires is .34, are being a ford and having good tires independent events?
Yes, they are independent because the probability of being a ford is the same as the probability of being a ford given that the car has good tires, which means that it is independent [P(A) and P(B) are independent if P(A|B) = P(A)]
