🌳 Conditional Probability & Independent Trials Lab
What you draw first changes what comes next
Use a tree diagram for drawing without replacement to see conditional probability, then find out about independent trials — calculating the probability of exactly a certain number of successes when you repeat the same trial several times.
Draw a ball from a bag and, without putting it back, draw one more. The probability of the second draw depends on what you drew first. A probability recalculated like this, under the condition that something has already happened, is called conditional probability.
The opposite case — like flipping a coin or rolling dice, where the previous result has no effect at all on the next one — is called an independent trial. The probability of exactly k successes out of n trials is found by multiplying the number of ways to arrange the successes (nCk) by the probability of success and failure.
Change the number of balls in the tree diagram and watch conditional probability branch out, then use the sliders to change n, k, and p and see how the probability distribution of independent trials changes.
Draw one ball from the bag, don't put it back, and draw one more. Change the number of red and blue balls with the sliders, and see how the second draw's probability changes depending on what you drew first.
Red balls3
Blue balls2
P(2nd=red | 1st=red) vs P(2nd=red | 1st=blue)
If a player has a shooting-success probability of p, the probability of exactly k successes out of n independent shots is nCk×p^k×(1−p)^(n−k). Use the sliders to change n, k, and p and see how the probability distribution changes.