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

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 update:
- 2002-12-12 23:27
- Author:
- snoofer
- Revision:
- 1.1

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