There are two containers, with one containing 4 red and 3 green balls and other containing 3 blue and 4 green balls. One ball is drawn at random from each container. The probability that one of the the balls is red and the other is blue will be
A17
B\(\frac { 9 }{ 49 } \)
C\(\frac { 12 }{ 49 } \)
D\(\frac { 3 }{ 7 } \)
Question - 2
Two coins are simultaneously tossed. The probability of two heads simultaneously appearing is
A\(\frac { 1 }{ 8 } \)
B\(\frac { 1 }{ 6 } \)
C\(\frac { 1 }{ 4 } \)
D\(\frac { 1 }{ 2 } \)
Question - 3
Three values of x and y are to be fitted in a straight line in the form y=1+bx by the method of least squares. Give \(\sum { x=6, } \sum { y=21, } \sum { { x }^{ 2 } } =14\quad and\quad \sum { xy=46 } \)the value of a and b are respectively
A2 and 3
B1 and 2
C2 and 1
D3 and 2
Question - 4
The standard deviation of spot speed of vehicles in, a highway is 8.8km/h and the mean speed of the vehicles is 33km/h the coefficient of variation in speed is
A0.1517
B0.1867
C0.2666
D0.3646
Question - 5
A hydraulic structure has four gates which operate independently. The probability of failure of each gate is 0.2. Given that gate 1 has failed, the probability that both gates 2 and 3 will fail is
A0.240
B0.200
C0.040
D0.008
Question - 6
If P and Q are two random events, then which of the following is true?
AIndependence of P and Q implies that probability (P\(\cap \)Q)=0
CIf P and Q are mutually exclusive, then they must be independent
DProbability (P\(\cap \)Q)\(\le \)Probability (P)
Question - 7
A box contains 4 white balls and 3 red balls. In succession, two balls randomly selected and removed from the box. Given that the first removed ball is white, the probability that the second removed ball is red, is
A\(\frac { 1 }{ 3 } \)
B\(\frac { 3 }{ 7 } \)
C\(\frac { 1 }{ 2 } \)
D\(\frac { 4 }{ 7 } \)
Question - 8
Assume for simplicity that N people, all born in April (a month of 30 days) are collected in a room. Consider, the event of atleast two people in the room being born on the same date of the month, even in different years, e.g., 1980 and 1985. What is the smallest N. So that the probability of this event exceeds 0.5?
A20
B7
C15
D16
Question - 9
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
Asame as that of occurrence 3, 4, 5
Bsame as that of occurrence 1, 2, 5
C\(\frac { 1 }{ 128 } \)
D\(\frac { 5 }{ 8 } \)
Question - 10
A fair coin is tossed three times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is