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Probability Part 3 , GATE Questions, Mathematics, Electrical Engineering, GATE Video Lecture

FAQs on Probability Part 3 , GATE Questions, Mathematics, Electrical Engineering, GATE Video Lecture

1. What is the probability of getting two heads when flipping a fair coin twice?
Ans. The probability of getting a head on any single coin flip is 1/2. Therefore, the probability of getting two heads in a row is (1/2) * (1/2) = 1/4.
2. If two dice are rolled simultaneously, what is the probability of getting a sum of 7?
Ans. To get a sum of 7, there are 6 possible outcomes: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). Since there are a total of 36 possible outcomes when rolling two dice, the probability of getting a sum of 7 is 6/36 = 1/6.
3. A bag contains 3 red balls, 4 green balls, and 5 blue balls. If a ball is drawn at random, what is the probability that it is not red?
Ans. The total number of balls in the bag is 3 + 4 + 5 = 12. Since there are 3 red balls, the probability of drawing a red ball is 3/12 = 1/4. Therefore, the probability of not drawing a red ball is 1 - 1/4 = 3/4.
4. A spinner with four equal sectors labeled A, B, C, and D is spun twice. What is the probability of landing on sector A both times?
Ans. The probability of landing on sector A in a single spin is 1/4. Since the spins are independent events, the probability of landing on sector A both times is (1/4) * (1/4) = 1/16.
5. A box contains 8 red marbles and 12 blue marbles. If two marbles are drawn without replacement, what is the probability of getting two red marbles?
Ans. The probability of drawing a red marble on the first draw is 8/20. After removing one red marble, the probability of drawing another red marble on the second draw is 7/19. Therefore, the probability of getting two red marbles without replacement is (8/20) * (7/19) = 56/380 = 7/47.
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