JEE Main Mathematics - Probability
Exam Duration: 60 Mins Total Questions : 30
The probability that a leap year has 53 sundays
- (a)
\(\cfrac { 1 }{ 7 } \)
- (b)
\(\cfrac { 2 }{ 7 } \)
- (c)
\(\cfrac { 3 }{ 7 } \)
- (d)
\(\cfrac { 4 }{ 7 } \)
The probability of a five-digit number formed by the digits 0, 1, 2, 3, 4 which is divisible by 4 is
- (a)
\(\cfrac { 5 }{ 16 } \)
- (b)
\(\cfrac { 3 }{ 8 } \)
- (c)
\(\cfrac { 7 }{ 16 } \)
- (d)
\(\cfrac { 9 }{ 16 } \)
A, B, C are three events, such that P(B)=\(\cfrac { 3 }{ 4 } \) ,\(P(A\cap B\cap \overline { C } )=\cfrac { 1 }{ 3 } \) and \(P(\overline { A } \cap B\cap \overline { C } )=\cfrac { 1 }{ 3 } \) then \(P(B\cap C)\) equals
- (a)
\(\cfrac { 1 }{ 12 } \)
- (b)
\(\cfrac { 1 }{ 6 } \)
- (c)
\(\cfrac { 1 }{ 15 } \)
- (d)
\(\cfrac { 1 }{ 9 } \)
A box contains 25 tickets numbered 1 to 25. Two tickets are drawn at random. The probability of their product being even is
- (a)
\(\cfrac { 11 }{ 50 } \)
- (b)
\(\cfrac { 13 }{ 50 } \)
- (c)
\(\cfrac { 37 }{ 50 } \)
- (d)
NONE OF THESE
The probability that atleast one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then \(P(\overline { A } )+P(\overline { B } )\) is
- (a)
0.4
- (b)
0.8
- (c)
1.2
- (d)
1.4
If A and B are any two events, such that P(A)=0.9, P(B)=0.8 and \(P(A\cap B)\ge k\), then k equals
- (a)
0.6
- (b)
0.5
- (c)
0.7
- (d)
0.85
In a leap year, the probability of having 53 Sunday or 53 Monday is
- (a)
2/7
- (b)
3/7
- (c)
4/7
- (d)
5/7
Let 0<P(A)<1, 0<P(B)<1 and P(\(A\cup B\))=P(A)+P(B)-P(A).P(B). Then,
- (a)
\(P({B\over A})=P(B)-P(A)\)
- (b)
\(P(A^c\cup B^c)=P(A^c)+P(B^c)\)
- (c)
\(P(A\cup B)^c=P(A^c).P(B^c)\)
- (d)
\(P({A\over B})={P({B\over A})}\)
Word 'UNIVERSITY' is arranged randomly, then the probability that both 'I' are not together, is
- (a)
3/5
- (b)
2/5
- (c)
4/5
- (d)
3/5
If A and B are two independent events such that \(P(\bar{A})={7\over 10}\), \(P(\bar B)=\alpha\) and \(P(A\cup B)={4\over5}\) then the value of \(\alpha\) is
- (a)
1
- (b)
\(5\over7\)
- (c)
\(2\over7\)
- (d)
\(1\over4\)
An urn contains nine balls of which three are red, our are blue and two are green. Three balls are drawn at random without replacement from the run. The probability that the three balls have different colours, is
- (a)
\(1\over 3\)
- (b)
\(2\over 7\)
- (c)
\(1\over21\)
- (d)
\(2\over23\)
A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then, \(P(A\cup B)\) is
- (a)
\(2\over5\)
- (b)
\(3\over5\)
- (c)
0
- (d)
1
The coefficients of a quadratic equation \({ ax }^{ 2 }+bx+c=0\quad (a\neq b\neq c)\) are chosen from first three prime numbers, the probability that roots of the equation are real is
- (a)
1/3
- (b)
2/3
- (c)
1/4
- (d)
3/4
The decimal parts of the logarithms of two numbers taken at random are found to six places. Probability that second can be subtracted from one first without borrowing is
- (a)
\(\left( \frac { 1 }{ 2 } \right) ^{ 6 }\)
- (b)
\(\left( \frac { 9 }{ 20 } \right) ^{ 6 }\)
- (c)
\(\left( \frac { 11 }{ 20 } \right) ^{ 6 }\)
- (d)
\(\left( \frac { 3 }{ 20 } \right) ^{ 6 }\)
The probability that a teacher will give an unannounced test during any class meeting is 1/5. If a student is absent twice, the probability that he will miss atleast one test, is
- (a)
7/25
- (b)
9/25
- (c)
16/25
- (d)
24/25
A box contains cards numbered 1 to 100. A card is drawn at random from the box. The probability of drawing a number which is a square, is
- (a)
1/5
- (b)
2/5
- (c)
1/10
- (d)
none of these
A three-digit number is selected at random from the set of all three-digit numbers. The probability that the number selected has all the three digits same, is
- (a)
1/9
- (b)
1/10
- (c)
1/50
- (d)
1/100
A die is thrown 2n + 1 times, n \(\in \) N. The probability that faces with even numbers show odd number of times is
- (a)
\(\frac { 2n+1 }{ 2n+3 } \)
- (b)
less than \(\frac { 1 }{ 2 } \)
- (c)
greater than 1/2
- (d)
none of these
Sixteen players P1 , P2, ...P16 play in a tournament. They are divided into eight pairs at random. From each pair a winner is decided on the basis of a game played between the two players of the pair. Assuming that all the players are of equal strength, the probability that exactly one of the two players P1 and P2 is among the eight winners is
- (a)
4/15
- (b)
7/15
- (c)
8/15
- (d)
17/30
Let X be a set containing n elements. If two subsets A and B of X are picked at random, the probability that A and B have the same number of elements is
- (a)
\(\frac { ^{ 2n }{ { C }_{ n } } }{ { 2 }^{ 2n } } \)
- (b)
\(\frac { 1 }{ ^{ 2n }{ { C }_{ n } } } \)
- (c)
\(\frac { 1.3.5...(2n-1) }{ { 2 }^{ n }.n! } \)
- (d)
\(\frac { { 3 }^{ n } }{ { 4 }^{ n } } \)
Three six faced fair dice are thrown together. The probability that the sum of the numbers appearing on the dice is k(3\(\le \)k\(\le \)8) is
- (a)
\(\frac { (k-1)(k-2) }{ 432 } \)
- (b)
\(\frac { k(k-2) }{ 432 } \)
- (c)
\(^{ k-1 }{ { C }_{ 2 } }\times \frac { 1 }{ 216 } \)
- (d)
\(\frac { k^{ 2 } }{ 432 } \)
If a particular experiment be given n (a finite) independent trials.
If the probability of success in one trial (say) p
\(\therefore\) We get probability of failure, q = (1 - p)
The probability of r success in n trials =nCrprqn-r
In a lot containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is
- (a)
10-15
- (b)
\({ \left( \frac { 1 }{ 5 } \right) }^{ 5 }\)
- (c)
\({ \left( \frac { 9 }{ 10 } \right) }^{ 5 }\)
- (d)
\(\frac { 9 }{ 10 } \)
The probabilities that a student in Mathematics, Physics and Chemistry \(\alpha \) ,\(\beta \) and \(\gamma \)respectively. Of these subjects, a student has a 75% chance of passing in atleast one, a 50% chance of passing in atleast two and a 40% chance of passing in exactly two subjects. Which of the following relations are true?
- (a)
\(\alpha +\beta +\gamma =19/20\)
- (b)
\(\alpha +\beta +\gamma =27/20\)
- (c)
\(\alpha \beta \gamma =1/10\)
- (d)
\(\alpha \beta \gamma =1/4\)
A box contains 1 red and 3 identical blue balls. Two balls are drawn at random in succession without replacement. Then, the sample space for this experiment is
- (a)
{RB, BR, BB}
- (b)
{R, B, B}
- (c)
{RB}
- (d)
{RB, BR}
Two dice are thrown. The events P, Q and R are described as follows:
P: getting an odd number on the first die.
Q: getting an even number on the first die.
R: getting atmost 6 as sum of the numbers on two dice.
The total number of outcomes in the event (P or R) is
- (a)
20
- (b)
24
- (c)
21
- (d)
23
Two dice are thrown. The events P, Q and R are described as follows:
P: getting an odd number on the first die.
Q: getting an even number on the first die.
R: getting atmost 6 as sum of the numbers on two dice.
The set of the event (Q and R) is
- (a)
{(2, 1), (2,2), (2, 3)}
- (b)
{(3, 1),(4, 1)}
- (c)
{(2, 1), (2,2)(2,3), (4, 1)}
- (d)
None of these
A coin is tossed three times, consider the following events
A : no head appear.
B : exactly one head appear.
C : atleast two heads appear.
Then,
- (a)
A, Band C are mutually exclusive events
- (b)
A, Band C are exhaustive events
- (c)
Only (a)
- (d)
Both (a) and (b)
Which of the following cannot be the probability of occurrence of an event?
- (a)
0
- (b)
\(\frac{1}{2}\)
- (c)
\(\frac{3}{4}\)
- (d)
\(\frac{4}{3}\)
In a relay race there are five teams A, B, C, D and E. Answer the following questions.
What is the probability that A, Band C finish first, second and third, respectively?
- (a)
1/12
- (b)
1/60
- (c)
1/10
- (d)
1/6
If A and B are mutually exclusive events, then
- (a)
P(A)\(\le \)P(B)
- (b)
P(A)\(\ge \)P(B)
- (c)
P(A) < P(B)
- (d)
None of these