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

Added by: snoofer 

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!