If a seed is planted, it has a 75% chance of growing into a healthy plant.

If 6 seeds are planted, what is the probability that exactly 1 doesn't grow?

9.72405%

Step-by-step explanation:

Binomial Probability

(N choose k) p^k (1-p) ^ (n-k)

N=7 seeds planted

p = 100% - 70% = 30% = 0.3 <-- - we are interested in the plant NOT growing

(1-p) = 70% = 0.7 <-- - 70% chance the plant will survive and grow

k=4 <-- - we want four of them to fail

The probability is:

(7 choose 4) * (0.3) ^4 (0.7) ^3 =

7! / (4!3!) (0.3) ^4 (0.7) ^3 =

(7*6*5/3*2) (0.3) ^4 (0.7) ^3 =

7*5 (0.3) ^4 (0.7) ^3 =

35 * 0.0081 * 0.343 = 0.0972405 = 9.72405%