Garden centre

A garden centre sells seedlings of not yet bloomed roses. From long-term experience it is known that 91% of these seedlings bloom red, but the remaining seedlings do not bloom at all. The average lifespan of a seedling is 36 hours. The roses are sold in boxes of 6 pieces. The costs per one box are 90 euros, it is sold for 135 euros, but at the same time the garden centre committed that if more than one rose blooms differently than red, it will return the customer's money for all the seedlings.
What is the probability that the garden centre will achieve a profit of 50%? (I.e. that in no box do more than one seedling bloom differently than red?)
(Write the resulting probability in percents.)

Final Answer:

p =  90.48 %

Step-by-step explanation:

$$\begin{gathered} p_1=91\%=\frac{91}{100}=0.91 \\ {p}_2=1-p_1=1-0.91=\frac{9}{100}=0.09 \\ {P}_0=\left(\genfrac{}{}{0ex}{}{6}{0}\right)\cdot p_2^0\cdot (1-p_2{)}^{6-0}=(\genfrac{}{}{0ex}{}{6}{0})\cdot 0.09^0\cdot (1-0.09{)}^{6-0}=1\cdot 0.09^0\cdot 0.91^6\doteq 0.5679 \\ {P}_1=\left(\genfrac{}{}{0ex}{}{6}{1}\right)\cdot p_2^1\cdot (1-p_2{)}^{6-1}=(\genfrac{}{}{0ex}{}{6}{1})\cdot 0.09^1\cdot (1-0.09{)}^{6-1}=6\cdot 0.09^1\cdot 0.91^5\doteq 0.337 \\ {P}_{10}=P_0+P_1=0.5679+0.337\doteq 0.9048 \\ z=\frac{135}{90}=\frac{3}{2}=1.5 \\ p=100\cdot P_{10}=100\cdot 0.9048=90.48\% \end{gathered}$$

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