MATH SOLVE

3 months ago

Q:
# There are 6 red marbles, 4 blue marbles, and 6 yellow marbles in a bag. A total of 2 marbles are chosen without replacing them. What is the probability of first choosing a yellow marble and then choosing a blue marble?

Accepted Solution

A:

In total, there are 16 marbles.So the probability of first choosing a yellow marble is: [tex]\frac{6}{16}[/tex] (That's because in our bag if 16 marbles, 6 of them are yellow)However, as stated in the question, we do not replace the marble.That means we will now only have bag of 15 marbles in total (since we have already taken out the first marble)So the probability of then choosing a blue marble is:[tex]\frac{4}{15}[/tex] (that's because in our bag of 15 marbles, 4 of them are blue)----------------------------------------------Finally to get the answer we multiply the two probabilities that we worked out. That's because in probability, and = multiplySo P(choosing a yellow marble) and P(choosing a blue marble)= P(choosing a yellow marble) times P(choosing a blue marble)So the final probability is:[tex]\frac{6}{16}[/tex] × [tex]\frac{4}{15}[/tex] = [tex]\frac{24}{240}[/tex]This simplifies down to [tex]\frac{1}{10}[/tex]------------------------------------------------------Answer:The probability of first choosing a yellow marble and then a blue marble is:[tex]\frac{1}{10}[/tex]