Question

a bag contains 4 blue marbles, 6 orange marbles, and 3 yellow marbles. select the expression that shows the probability of randomly drawing an orange marble followed by a yellow marble without replacement. question 2 (multiple choice worth 5 points) (conditional probability lc)

Explanation:

Step1: Calculate total number of marbles

Total marbles = \(4 + 6+3=13\)

Step2: Calculate probability of drawing an orange marble

Probability of first - draw (orange) \(P(O_1)=\frac{6}{13}\)

Step3: Calculate probability of drawing a yellow marble after an orange marble (without replacement)

After drawing an orange marble, total marbles left \(n = 12\), yellow marbles \(y = 3\). Probability \(P(Y|O)=\frac{3}{12}\)

Step4: Use the formula for conditional probability \(P(A\cap B)=P(A)\times P(B|A)\)

Here \(A\) is the event of drawing an orange marble and \(B\) is the event of drawing a yellow marble. So the probability is \(\frac{6}{13}\times\frac{3}{12}\)

Answer:

\(\frac{6}{13}\times\frac{3}{12}\)