Question

if the probability of a thunderstorm today is \\(\frac{2}{9}\\), then what is the complement or the probability of it not thunderstorming today?

a.) \\(\frac{1}{9}\\)

b.) \\(\frac{7}{9}\\)

c.) \\(\frac{9}{7}\\)

d.) \\(\frac{9}{2}\\)

Explanation:

Identify the probability of the event

$$ P(\text{Thunderstorm}) = \frac{2}{9} $$

Apply the complement rule for probability

$$ P(\text{Not Thunderstorm}) = 1 - P(\text{Thunderstorm}) = 1 - \frac{2}{9} $$

Calculate the final value

$$ P(\text{Not Thunderstorm}) = \frac{9}{9} - \frac{2}{9} = \frac{7}{9} $$

Answer:

• a.) \(\frac{1}{9}\)
• b.) \(\frac{7}{9}\) (Correct answer)
• c.) \(\frac{9}{7}\)
• d.) \(\frac{9}{2}\)