In Europe, 53% of flowers of the rewardless orchid, Dactylorhiza sambucina are yellow, whereas the remaining flowers are purple (Gigord et al. 2001). If we took a random sample of five individuals, what is the probability that at least three would be yellow? Include the leading zero, and state your answer to three decimal places.

Probability that at least three would be yellow = 0.556 .

Step-by-step explanation:

We are given that In Europe, 53% of flowers of the reward less orchid, Dactylorhiza sambucina are yellow.

The Binomial distribution probability is given by;

P(X = r) = for x = 0,1,2,3,.......

Here, n = number of trials which is 5 in our case

          r = no. of success which is at least 3 in our case

         p = probability of success which is probability of yellow flower of

                0.53 in our case

So, P(X >= 3) = P(X = 3) + P(X = 4) + P(X = 5)

      =

      =

      = 0.556

Therefore, the probability that at least three would be yellow is 0.556 .        

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