41. A fair dice is rolled twice. The probability that an odd number will follow an even number is
42. Two bags A and B have equal number of bails. Bag A has 20% red balls and 80% green bails. Bag B has 30% red bails. 60% green balls and 10% yellow balls. Contents of Bags A and B are mixed thoroughly and a ball is randomly picked from the mixture. What is the chance that the ball picked is red?
43. If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?
44. If the standard deviation of the spot speed of vehicles in a highway is 8.8 kmph and the mean speed of the vehicles is 33 kmph, the coefficient of variation in speed is
45. Which one of the following statements is NOT true?
46. The probability that a thermistor randomly picked up from a production unit is defective is 0.1. The probability that out of 10 thermistors randomly picked up, 3 are defective is
47. In a game, two players X and Y are tossing a coin alternately. Whoever gets a 'head' first, wins the game and the game is terminated. Find the chance that player X will win the game if he starts?
48. A loaded dice has following probability distribution of occurrences
Dice Value
1
2
3
4
5
6
Probability
$$\frac{1}{4}$$
$$\frac{1}{8}$$
$$\frac{1}{8}$$
$$\frac{1}{8}$$
$$\frac{1}{8}$$
$$\frac{1}{4}$$
If three identical dice as the above are thrown, the probability of occurrence of values 1, 5 and 6 on the three dice is
| Dice Value | 1 | 2 | 3 | 4 | 5 | 6 |
| Probability | $$\frac{1}{4}$$ | $$\frac{1}{8}$$ | $$\frac{1}{8}$$ | $$\frac{1}{8}$$ | $$\frac{1}{8}$$ | $$\frac{1}{4}$$ |
If three identical dice as the above are thrown, the probability of occurrence of values 1, 5 and 6 on the three dice is
49. Consider a Gaussian distributed random variable with zero mean and standard deviation σ. The value of its cumulative distribution function at the origin will be
50. Two independent random variables X and Y are uniformly distributed in the interval [-1, 1]. The probability that max [X, Y] is less than $$\frac{1}{2}$$ is
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