I don’t understand how the teacher solved the problem here, what’s the logic behind it and how Pascal's triangle is useful here. Also what is the difference between nPr and nCr?
#Pascal's triangle with probability?
wraith plinth
ocean quartz
p would be the probability he will win, in this case if he draws 1 or 2 out of 6 numbers, so p = 2/6 = 1/3
q is basically the probability he doesn't win q = 1 - p = 2/3
ocean quartz
I don’t understand how the teacher solved the problem here, what’s the logic beh...
how your teacher solved it here is by making the problem into a binomial one
a binomial probability is when the following conditions are met
- finite no. of tries
- exactly 2 possible outcomes (in this case, win or no win)
- the probability of success (or winning) [p] is constant for each trail (conversely the probability of failure [q] is also constant)
- the trails are independent of each other
general formula
Let X ~ B(n, r) denote the number of successes out of n trails
P(X = r) = nCr(p^r)(q^n-r)
- r is no. success
- p is probability of success
- n is no. trails
- q is probability of failure
hence in this case
Let X ~ B(4, 1/3) denote the number of wins out of 4 trails
the probability that he wins twice in 4 tries,
P(X = 2) = 4C2(1/3)^2 (2/3)^2