Question about Binomial Distribution

Question

The chance of a rose flower blooming is $.28$. You are going to plant $5$ rose flowers, what are the chances of $4$ of them blooming?

I was thinking the answer would be $35$% since $28\%*5=140$ and $\frac{140}{4}=35$. Is this correct?

Answer 1

It's a problem about binomial distribution $(n=5,p=.28)$.

4 roses which will bloom out of 5 can be chosen in ${5 \choose 4} = 5$ ways. So, the probability that 4 flowers will be bloomed and 1 will not be bloomed(prob. = 1-.28=.72) is,$$5*{.28}^4*.72=0.022127616$$

Answer 2

There are 6 cases to note here. There are 5 cases where 4 bloom and one doesn't along with the case of all 5 blooming.

The probability of all 5 blooming is $.28^5 = 0.0017210368$

The probability of exactly 4 blooming is $.28^4*.72 = 0.0044255232$

Now, take 5 times the last result is $0.022127616$ that can be combined with the other result giving a total of $0.0238486528$ or 2.4%