Question

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.

Answer 1

Answer:

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) = $\binom{n}{r}p^{r}(1-p)^{n-r}$ 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)

      = $\binom{5}{3}0.53^{3}(1-0.53)^{5-3} + \binom{5}{4}0.53^{4}(1-0.53)^{5-4} + \binom{5}{5}0.53^{5}(1-0.53)^{5-5}$

      = $10*0.53^{3}(0.47)^{2} + 5*0.53^{4}(0.47)^{1} + 1*0.53^{5}(0.47)^{0}$

      = 0.556

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