Mechanical Engineering > General Aptitude for GATE > Example: Marbles drawn (probability)
Example: Marbles drawn (probability) Video Lecture - General Aptitude for GATE - Mechanical Engineering
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FAQs on Example: Marbles drawn (probability) Video Lecture - General Aptitude for GATE - Mechanical Engineering
| 1. What is the probability of drawing a red marble from a bag containing 5 red marbles and 10 blue marbles? |  |
Ans. To find the probability of drawing a red marble, we need to divide the number of favorable outcomes (red marbles) by the total number of possible outcomes (red and blue marbles). In this case, the probability would be 5/15 or 1/3.
| 2. If I draw two marbles without replacement, what is the probability of drawing two blue marbles from a bag containing 5 red marbles and 10 blue marbles? | |
Ans. When drawing without replacement, the probability of the second event depends on the outcome of the first event. To find the probability of drawing two blue marbles, we multiply the probability of drawing a blue marble on the first draw (10/15) by the probability of drawing a blue marble on the second draw, given that the first marble was blue (9/14). Therefore, the probability would be (10/15) * (9/14) = 3/7.
| 3. What is the probability of drawing at least one red marble from a bag containing 5 red marbles and 10 blue marbles if three marbles are drawn without replacement? | |
Ans. To find the probability of drawing at least one red marble, we can calculate the probability of the complement event, which is drawing no red marbles. On the first draw, the probability of drawing a blue marble is 10/15. On the second draw, given that the first marble was blue, the probability of drawing another blue marble is 9/14. Similarly, on the third draw, the probability of drawing a blue marble is 8/13. Therefore, the probability of drawing no red marbles is (10/15) * (9/14) * (8/13). To find the probability of drawing at least one red marble, we subtract the probability of drawing no red marbles from 1. Hence, the probability would be 1 - (10/15) * (9/14) * (8/13).
| 4. If I want to maximize the probability of drawing a red marble from a bag containing 5 red marbles and 10 blue marbles, how many marbles should I draw? | |
Ans. To maximize the probability of drawing a red marble, you should draw all the marbles from the bag. Since there are 5 red marbles and 10 blue marbles, drawing all 15 marbles would guarantee that you draw a red marble.
| 5. What is the probability of drawing a blue marble from a bag containing 5 red marbles and 10 blue marbles if two marbles are drawn with replacement? | |
Ans. When drawing with replacement, each draw is independent, and the probability remains the same for each event. Therefore, the probability of drawing a blue marble on the first draw is 10/15, and the probability of drawing a blue marble on the second draw is also 10/15. Hence, the probability of drawing a blue marble on both draws is (10/15) * (10/15).
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Timeline
| 00:04 | Probability Problem - Marbles are drawn (both same color) |
| 00:36 | Scenario 1 - Pick one marble after the other |
| 01:47 | Scenario 2 - Pick - replace - pick |
| 02:41 | Probability Problem - Marbles are drawn (both different color) |
| 03:01 | Scenario 1 - Pick one marble after the other |
| 04:02 | Scenario 2 - Pick - replace - pick |
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