Probability of finding a specific colored plant in a row.

Question

In a packet of flower seeds 3/4 are yellow flowering and rest are white. If 200 rows of each plants are planted, how many will contain (i) all yellow flowers. (ii) all white flowers (iii) two yellow and two white flowers

Answer 1

I will assume that you mean a row is four flowers, and that the order on a row is not important. Then each row may be one in $5$ outcomes:

• (#yellow, #white) = {(4,0), (3,1), (2,2), (1,3), (0,4)}

If you bag of seeds is infinitely big, then taking a seed will not change the stated probabilities. Thus, we may use the binomial distribution.

The probabilities for all yellow and all white are pretty trivial, namely $0.75^4 = 0.3164$ and $0.25^4 = 0.0039$ respectively.

The probability of 2 of each is found by the binomial distribution: $\binom{2}{4} 0.75^2 0.25^2 = 0.2109$.

Out of 200 rows you simply multiply each probability by 200, then you will see the expected number of rows of each kind.

This may not be what you are looking for, as the question is very ambiguous...