Question

A jar contains 10 red marbles, 5 blue marbles, and 15 yellow marbles. All marbles are of the same shape and size and are equally likely to get picked. Find the probability of drawing a blue marble and then drawing a yellow marble randomly.

• A. $\frac{15}{58}$
• B. $\frac{5}{29}$
• C. $\frac{5}{58}$
• D. $\frac{15}{29}$

Answer 1

The correct option is C $\frac{5}{58}$

Given, Number of red marbles $=10$
Number of blue marbles $=5$
Number of yellow marbles $=15$
Total number of marbles $=10+5+15=30$
So, initially, there are 30 marbles and one marble is picked.
Now, the marble picked first is removed. There is a reduction in the number of elements in the sample space by 1.
So number of marbles left in the jar $=30-1=29$
Total number of possible outcomes for picking two marbles one after the other (the marble picked first is removed) $=30\times 29=870$
Number of ways in which a blue marble is picked first and then a yellow marble $=5\times 15=75$
This is the number of favorable outcomes.
So, the probability of drawing a blue marble and then drawing a yellow marble $=\frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}=\frac{75}{870}=\frac{5}{58}$