Question

suppose a jar contains 18 red marbles and 40 blue marbles. if you reach in the jar and pull out 2 marbles at random, find the probability that both are red. write your answer as a reduced fraction.
answer:

Explanation:

Step1: Calculate total number of marbles

The total number of marbles is the sum of red and blue marbles. So, $18 + 40=58$ marbles.

Step2: Calculate probability of first - red marble

The probability of picking a red marble on the first draw is $\frac{18}{58}$.

Step3: Calculate probability of second - red marble

After drawing one red marble, there are $17$ red marbles left and $57$ marbles in total. So the probability of picking a red marble on the second draw is $\frac{17}{57}$.

Step4: Calculate probability of both red marbles

Since these are independent - like events (in the sense of sequential drawing without replacement), we multiply the probabilities of each event. So the probability that both marbles are red is $\frac{18}{58}\times\frac{17}{57}=\frac{18\times17}{58\times57}=\frac{306}{3306}=\frac{51}{551}$.

Answer:

$\frac{51}{551}$