Question

suppose a jar contains 19 red marbles and 33 blue marbles. if you reach in the jar and pull out 2 marbles at random without replacement, find the probability that both are red. give your answer as a fraction or decimal out to at least 4 places.

Explanation:

Step1: Calculate the total number of marbles

The total number of marbles is \(19 + 33=52\) marbles.

Step2: Calculate the probability of drawing the first red marble

The probability of drawing the first red marble is \(\frac{19}{52}\).

Step3: Calculate the probability of drawing the second red marble

After drawing one red marble, there are \(19 - 1 = 18\) red marbles left and \(52- 1=51\) marbles left. So the probability of drawing the second red marble is \(\frac{18}{51}\).

Step4: Calculate the probability of both events

Using the multiplication rule for dependent events \(P(A\cap B)=P(A)\times P(B|A)\), the probability that both marbles are red is \(\frac{19}{52}\times\frac{18}{51}\).

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Answer:

\(\frac{57}{442}\approx0.129\)