Question

Suppose a jar contains 15 red marbles and 19 blue marbles. if you reach in the jar and pull out 2 marbles at random (first choose one, then, without replacement, choose the second one), find the probability that both are red. round your answer to 4 decimal places.

Answer 1

The probability of drawing two red marbles from a jar with 15 red and 19 blue marbles, without replacement, is approximately 0.1849.

Step-by-step explanation:

To find the probability that both marbles drawn from a jar containing 15 red marbles and 19 blue marbles are red, we use the basic principle of probability which says that the probability of an event is the number of favourable outcomes divided by the number of all possible outcomes. In this case, the event of drawing two red marbles one after the other without replacement involves the following steps:

1. Calculate the probability of drawing a red marble on the first draw. Since there are 15 red marbles and a total of 34 marbles (15 red + 19 blue), the probability is 15/34.
2. After drawing one red marble, there are now 14 red marbles left and 33 marbles in total. The probability of drawing a second red marble is now 14/33.
3. Multiply these probabilities together to get the probability of drawing two red marbles in a sequence without replacement: (15/34) × (14/33)

If we do the math, the probability is approximately 0.1849 when rounded to four decimal places.