If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Lesson 1: Basic probability

# Simple probability: non-blue marble

In this example we are figuring out the probability of randomly picking a non-blue marble from a bag. Again, we'll have to think about the possible outcomes first. Created by Sal Khan.

## Want to join the conversation?

• Sal-
Why do you always say "a fair coin"...and then begin the question?
What defines a fair coin? Does this refer to a coin that is not weighed down on one side to make it land a certain way, or does this refer to something else? •   A fair coin just means the coin has equal chance of showing tail or head when flipped. 50-50.
• A fair coin is flipped 4 times. What is the probability of getting more than 2 heads? I found the answer using the hints, which told me to write out all the possible outcomes. Needless to say, it is far from convenient as methods go. Isn't there a simpler way for finding the answer? •   This problem can be solved using binimial distribution.
n = 4, Probabilitiy of getting a head = 1/2 probability of not getting a head = 1/2.

The binomial probability formula is,
P(x) = nCx px qn-x

p(x>2) = P(X=3) + P( X = 4)
= 4C3 (1/2)^3 (1/2)^1 + 4C4 (1/2)4 (1/2)^0

= 4(1/2)^4 + 1 (1/2)4

= (1/2)^4 (4+1)

= 1/16 (5)
= 5/16
• Hi Sal - We considered the area of outer circle but only circumference of the inner circle, should we not consider areas of both the circles ? in that case answer would be : 64 pi / 324 pi and not 16pi / 324 pi • I have a small question
Probability should always be in the form of fractions right ? then why do some books or solutions have their answers in the decimal form?or is it the other way around? • At around he says "infinite number of points" what doe s that mean? • By "infinite number of points" Sal means that you can always add points on the circle between points that you have on it, to infinity.

It's easier to see this on a one-dimensional line. If you have points (0,0) and (1,0), you can add (0.5, 0) which is half-way. Then you can add half the way between (0,0) and (0.5, 0), which is (0.25, 0) and so on. Because a line of any length has infinite points on it, a circle (in which we can draw line segments) does as well.

Because of that, you can't use the number of points to determine the probability that the point lies in the smaller circle. You have to use the area of the circles instead.

I hope this helps.

--Phi φ
• is permutation and combination a higher level of probability? • Permutations and combinations are operations to count. They are used to find probabilities, but are not probabilities. Remember that a probability is just a ratio of all desirable outcomes over the sample space. We can use permutations and combinations to find the number of desirable outcomes and the size of the sample space.
• 70% of adults in a European city say that they enjoy using public transportation. If a random sample of 8 adults is selected from the city, find the probability that exactly 3 adults respond that they enjoy using public transportation. • probability that an adult do not like PT = 100-70 = 30% = 0.3
no. of adults who should not like PT among random 8 = 5. => 5/8
therefore, the probability is 0.3*5/8= 15/80 [ANSWER]
PLEASE CORRECT ME IF I AM WRONG
if i solve the question other way, I am getting answer 21/80.
PLEASE LET ME KNOW THE ANSWER, SO THAT I CAN THINK UPON WHICH OF THE METHOD IS CORRECT AND WHY?
though i presume that the first method and answer is correct, because of some weird logic that will be difficult to explain, though this weird logic may be the fundamental one!!!
THANKS! :)   