Question

In a genetics experiment 5 flowers out of 8 were bicolor, and the rest were solid color. If 3 of the flowers are selected at random without replacement, what is the probability that all 3 are bicolor

Answer 1

The probability of the first flower being bi-color is 5/8. If the first flower selected is bi-color, the probability of the second selection being bi-color is 4/7. Also if the first 2 selections are bi-color, the probability of the third selection being bi-color is 3/6. Therefore the required probability is given by:
\[\large P(3\ bicolor)=\frac{5\times4\times3}{8\times7\times6}=you\ can\ calculate\]

Answer 2

or you can compare the number of possible "successful" outcomes to number of all possible outcomes
\[\frac{^{5}C_3}{^{8}C_3} \]which is the same thing

Answer 3

Thank you both