Three seeds each germinate with probability $ frac13$. The probabilit…

Question

Three seeds each germinate with probability $	frac13$. The probability that at least two germinate is:

Accepted Answer

B. $	frac{7}{27}$

1. 'At least two' covers exactly two germinating and all three germinating.
2. Exactly three: $\left(	frac13ight)^3=	frac1{27}$.
3. Exactly two: choose which two in 3 ways, giving $3	imes\left(	frac13ight)^2	imes	frac23=	frac6{27}$.
4. The two cases are mutually exclusive, so add them.
5. Total $=	frac6{27}+	frac1{27}=	frac7{27}$. Stopping at $	frac6{27}$ forgets the all-three branch of the tree diagram.
_Source: NECTA CSEE 2022 Basic Mathematics 041, Question 3: Sets and Probability_

Answer

$	frac{1}{27}$

Answer

$	frac{6}{27}$

Answer

$	frac{8}{27}$

Three seeds each germinate with probability $\tfrac13$. The probability that at least two germinate is:

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