A population of red-bellied snakes is known to have a ratio of grey color morph to red color morph of 53:47. You wish to know the probability of selecting a random sample of 30 snakes containing 10 or fewer red morph individuals. Use a statistical program to determine the exact probability of getting 10 or fewer grey morph individuals.

The probability is

Step-by-step explanation:

We know that the ratio of grey color morph to red color morph is

This can be written in terms of probability as :

This means that the probability of obtain a red color morph snake in a random sample of 100 snakes is (If I only randomly select one snake).

Now, the number of red color morph snakes in a random sample ''n'' can be modeled as a binomial random variable. Where ''p'' is the success probability (In our case, the probability from obtain one red color morph snake out of 100 snakes) ⇒

''Number of red color morph snakes in the sample''

In our case,

⇒ ~ Bi (n,p) ⇒ ~ Bi (30,0.47)

The probability function for is :

Where is the combinatorial number define as    ⇒

We need to calculate the probability of

This probability is equal to :

For example,

We need to calculate all the terms of the sum and then calculate

If we use any statistical program we will find that