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# What is the probability that I will have a female plant given X seeds?

 Added by: snoofer    Viewed: 308 times Rated by 12 users: 7.83/10 Contributed by: The White Rabbit Suppose that an experiment can have only 2 possible outcomes. This is known as a Bernoulli trial. In general the outcomes are success or failure. If P is the probability of success, and q is the probability of failure then p+q=1 Many Problems can be solved by determining the probability of k successes when an experiment consists of n independent Bernoulli trials. What we want to know is what is the probability of a success (female) given a certain number of experiments (seeds). Probability of k successes in n independent bernoulli trials with success as p and failure as q=1-p We will use a 50/50 success failure ratio, so p=.5 and q=.5 Probability of K successes = c(n,k)*p^k* q^(n-k) where; C(n,k) = n!/r!(n-r)! and n! is 'n factorial'. for example: 6! = 6*5*4*3*2*1 : 3! = 3*2*1 Probability of 1 success w/ 6 seeds is 9.3% Probability of 2 success w/ 6 seeds is 23.4% Probability of 3 success w/ 6 seeds is 31.25% Probability of 4 success w/ 6 seeds is 23.4% Probability of 5 success w/ 6 seeds is 9.3% Probability of 6 success w/ 6 seeds is 1.563% The sum of these gives the probability of getting at least 1 female from 6 seeds with 50% male female ratio is approx 98%. Now it is easier to find this by taking an alternate route. Simply calculate the probability of failure. That is the probability of 0 successes and subtracting that from 1. i.e. probability of 0 success w/ 6 seeds is 1.563% so probability of at least 1 success is 98.43% So the final equation we need is: 1 - C(n,0) * p^0 * q^(n-0) SO probability of at least 1 female plant: 1 seed: 50% 2 seed: 75% 3 seed: 87.5% 4 seed: 93.75% 5 seed: 96.875% 6 seed: 98.43% This example used a (50/50) male female ratio, but bernoulli trials allow insertion of different p's and q's for different male/female ratio's like (60/40) or whatnot. just make sure that p+q=1 in other words the probability of success plus failure = 100%. Modification of this concept can answer different questions just use creativity! Last modified: 23:27 - Dec 12, 2002
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