We are planting

We are planting 2 types of roses (white and red). Experience shows that the probability of a red rose sprouting is 0.7. A total of 5 seedlings are planted. What is the probability that:
a) the first 2 will be red and the next white
b) all will be red
c) none will be red
d) at least 1 white will bloom

Correct answer:

p₁ =  0.0132
p₂ =  0.1681
p₃ =  0.0024
p₄ =  0.8319

Step-by-step explanation:

$$\begin{gathered} c=0.7 \\ b=1-c=1-0.7=\frac{3}{10}=0.3 \\ {p}_1=c^2\cdot b^3=0.7^2\cdot 0.3^3=0.0132 \end{gathered}$$

$p_2=c^5=0.7^5=0.1681$

$p_3=b^5=0.3^5=0.0024$

$p_4=1-p_2=1-0.1681=0.8319$

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