Question

mr. patrick brought in 17 solid colored eggs to his physics classroom. 8 of the eggs were green and 5 were red. if mr. patrick randomly chose 5 eggs in a certain order for his first class to use in an egg drop experiment, what is the probability that the first 2 eggs are green and the last 3 are red? write your answer as a decimal rounded to four decimal places.

Explanation:

Step1: Calculate probability of first green egg

The probability of choosing a green egg first is $\frac{8}{17}$ since there are 8 green eggs out of 17 total eggs.

Step2: Calculate probability of second green egg

After choosing one green egg, there are 7 green eggs left and 16 total eggs left. So the probability of choosing a green egg second is $\frac{7}{16}$.

Step3: Calculate probability of first red egg

After choosing 2 green eggs, there are 5 red eggs and 15 total eggs left. So the probability of choosing a red egg third is $\frac{5}{15}$.

Step4: Calculate probability of second red egg

After choosing 3 eggs (2 green and 1 red), there are 4 red eggs and 14 total eggs left. So the probability of choosing a red egg fourth is $\frac{4}{14}$.

Step5: Calculate probability of third red egg

After choosing 4 eggs (2 green and 2 red), there are 3 red eggs and 13 total eggs left. So the probability of choosing a red egg fifth is $\frac{3}{13}$.

Step6: Calculate overall probability

The overall probability is the product of these individual probabilities: $\frac{8}{17}\times\frac{7}{16}\times\frac{5}{15}\times\frac{4}{14}\times\frac{3}{13}=\frac{8\times7\times5\times4\times3}{17\times16\times15\times14\times13}=\frac{3360}{742560}\approx0.0045$.

Answer:

0.0045