You are a farmer whose farmland is cool, moist, and shady. (assume that these growing conditions are equivalent to 80 drops/hr of water, 10% light, and a temperature of 13°c in the gizmo.) you are thinking about planting seeds like seed a in the gizmo. you will turn a profit if at least 50% of your seeds become sprouts. are you most likely to make money or lose money on this crop?

Define
n = number of seeds planted.
k = number of seeds that successfully become plants.

The probability of making a profit is
p =50% = 0.5
Therefore the probability of not makng a profit is
q = 1 - p = 0.5

According to the binomial distribution, the probability of k successes out of n trials is


Create a table as shown below by using the graphing calculator.

  n      k   P(k of n)
----  -----  ------------
  4      2    0.375
  8      4    0.273
 10     5    0.246
  12    6    0.226
  16    8    0.196
  20  10    0.176
  50  25   0.0.112
 100  50   0.08

A graph of this table shows that the probability of success i below 0.5 (50%) for all practical values of n (the number of seeds planted).

The farmer will lose money.