Question

suppose a jar contains 7 red marbles and 14 blue marbles. if you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Explanation:

Step1: Calculate the total number of marbles

The total number of marbles is \(7 + 14=21\) marbles.

Step2: Calculate the probability of pulling the first red marble

The probability of pulling the first red marble is \(\frac{7}{21}=\frac{1}{3}\)

Step3: Calculate the probability of pulling the second red marble

After pulling one red marble, there are \(7 - 1 = 6\) red marbles left and \(21- 1=20\) marbles left in total. So the probability of pulling the second red marble is \(\frac{6}{20}=\frac{3}{10}\)

Step4: Calculate the probability of both events happening

Since these are two - step dependent events, we use the multiplication rule for dependent events \(P(A\cap B)=P(A)\times P(B|A)\). So the probability that both marbles are red is \(\frac{7}{21}\times\frac{6}{20}\)

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Answer:

\(\frac{1}{10}\)