Question

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 20 snakes containing 3 or fewer grey morph individuals. use r to determine the exact probability of getting three or fewer grey morph individuals.

Answer 1

The exact probability of getting three or fewer grey morph individuals out of a sample of 20 snakes, we can use the binomial probability formula. The probability is approximately 0.1007.

Step-by-step explanation:

To calculate the exact probability of getting three or fewer grey morph individuals, we can use the binomial probability formula.

The formula is:

P(X ≤ k) = ∑(nCk * p^k * (1-p)^(n-k))

Where:

• P(X ≤ k) is the probability of getting k or fewer grey morph individuals
  
  
• n is the total sample size (20 snakes)
  
  
• k is the number of grey morph individuals (3)
  
  
• p is the probability of getting a grey morph individual (53/100 = 0.53)
  

Using this formula, we can calculate the probability as:

P(X ≤ 3) = ∑(20Ck * 0.53^k * (1-0.53)^(20-k))

P(X ≤ 3) = (20C0 * 0.53^0 * (1-0.53)^(20-0)) + (20C1 * 0.53^1 * (1-0.53)^(20-1)) + (20C2 * 0.53^2 * (1-0.53)^(20-2)) + (20C3 * 0.53^3 * (1-0.53)^(20-3))

P(X ≤ 3) = 0.0004 + 0.0046 + 0.0242 + 0.0715

P(X ≤ 3) = 0.1007