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Chapter 9: Problem 32

Find the probability for the experiment of drawing two marbles at random (without replacement) from a bag containing one green, two yellow, and three red marbles. Both marbles are yellow.

Short Answer

Expert verified
The probability of drawing two yellow marbles from the bag is \(\frac{1}{15}\).

Step by step solution

01

Calculate total number of possibilities

Calculate total possibilities for drawing 2 marbles from a bag of 6, which is a combination problem. We can use the combination formula \({n \choose r}\) = \(\frac{n!}{r!(n-r)!}\), where n is total number of items and r is items chosen at a time. So, total possibilities = \({6 \choose 2}\) = \(\frac{6!}{2!(6-2)!}\) = 15
02

Determine favorable outcomes

Next, calculate the number of ways we can draw 2 yellow marbles from the available 2 yellow marbles. Again, this is a combination problem. So, favorable outcomes = \({2 \choose 2}\) = \(\frac{2!}{2!(2-2)!}\) = 1.
03

Find the probability

The probability of an event is given by Probability = \(\frac{{favorable outcomes}}{{total outcomes}}\). So, the probability of drawing 2 yellow marbles = \(\frac{1}{15}\)

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Most popular questions from this chapter

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