Question

According to genetic theory, every plant of a particular species has a 25% chance of being red-flowering, independently of all other plants. Among 10 plants of this species, what is the chance that fewer than 4 are red-flowering?

My answer was 28431/1048576.
I did it like this:
The chance that there is 1 red and 9 others: 1/4 * (3/4)^9
The chance that there are 2 red and 8 others: 1/4 * 1/4 * (3/4)^8
The chance that there are 3 red and 7 others: 1/4 * 1/4 * 1/4 *(3/4)^7.
All the others added up made 28431/1048576.
But this is wrong. Anybody could give me a hint in the right directi

Answer 1

it is wrong because you also need the number of ways to get each out come

Answer 2

for example
one red and 9 others has nine ways it can happen

Answer 3

what you need is
\[P(x=k)=\binom{10}{k}(\frac{1}{4})^k(\frac{3}{4})^{n-k}\] you are missing the \(\binom{10}{k}\) part

Answer 4

actually i meant
\[P(x=k)=\binom{10}{k}(\frac{1}{4})^k(\frac{3}{4})^{10-k}\]

Answer 5

ahh the number of combinations ... stupid me! I will give it a shot

Answer 6

The results would be: 754515/1048576

Answer 7

The answer is not correct hmmm

Answer 8

Take this as bonus my friend : the answer is 0.775875.

Answer 9

you need the details ???? consult your binomial theory. you see the mean=np=10*(0.25)
then it goes on and on..............lol

Answer 10

binomial distribution:
p=0.25
n=10
X<=3