Question

you pick a card at random, put it back, and then pick another card at random. 5 6 7 8 9 what is the probability of picking a divisor of 40 and then picking a factor of 42? write your answer as a percentage rounded to the nearest tenth.

Explanation:

Step1: Find divisors of 40

Divisors of 40 among 5, 6, 7, 8, 9 are 5, 8. So probability of picking a divisor of 40, $P_1=\frac{2}{5}$.

Step2: Find factors of 42

Factors of 42 among 5, 6, 7, 8, 9 are 6, 7. So probability of picking a factor of 42, $P_2=\frac{2}{5}$.

Step3: Calculate combined probability

Since the two - card picks are independent events, the combined probability $P = P_1\times P_2=\frac{2}{5}\times\frac{2}{5}=\frac{4}{25}$.

Step4: Convert to percentage

$P=\frac{4}{25}\times100\% = 16.0\%$

Answer:

16.0%