Final answer:
The probability that both Amina and Bader were given sugar tablets is 22/145.
Step-by-step explanation:
To find the probability that both Amina and Bader were given sugar tablets, we need to calculate the probability of Amina getting a sugar tablet and then the probability of Bader getting a sugar tablet after Amina.
There are a total of 30 tablets in the box (18 vitamin and 12 sugar tablets). For Amina's selection, the probability of getting a sugar tablet is 12/30 = 2/5. After Amina takes a tablet, there are 29 tablets left, with 11 sugar tablets remaining. So, the probability of Bader getting a sugar tablet is 11/29.
To find the probability of both events happening, we multiply the probabilities together: (2/5) * (11/29) = 22/145.