Question 14
Suppose a jar contains 11 red marbles and 17 blue marbles. What is the probability that two
marbles drawn at random from the bag will both be red?
Write the probability as a decimal rounded to three decimal places.
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To solve this, we first need to determine the total number of marbles in the jar, which is 11 red + 17 blue = 28 marbles. The probability of drawing the first red marble is 11/28. Once the first red marble is drawn, there are now 10 red marbles left and a total of 27 marbles in the jar. Therefore, the probability of drawing a second red marble is 10/27. To find the overall probability of both events occurring, we multiply the two probabilities: (11/28) * (10/27) = 110/756 = 0.145. So, rounded to three decimal places, the probability is 0.145.

Did you know that probability theory dates back hundreds of years? It really took off in the 17th century, thanks to mathematicians like Blaise Pascal and Pierre de Fermat, who were trying to solve gambling problems. Their work laid the foundation for modern probability, turning a game of chance into a structured field of study that’s applied in everything from statistics to finance!

If you’re interested in diving deeper into probability, there are some great resources out there! “Introduction to Probability” by Dimitri P. Bertsekas and John N. Tsitsiklis offers a solid foundation. For a more hands-on approach, check out “Naked Statistics” by Charles Wheelan—it’s engaging and breaks down complex concepts in a way that’s easy to understand. Happy learning!