## Probability Quiz-1

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.

Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced.

Q1. Two events A and B have probability 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14. Then, the probability that neither A nor B occur, is
•  0.39
•  0.25
•  0.11
•  None of these
Solution
(a) P(A)=0.25,
P(B)=0.50,
P(A∩B)=0.14
P(A∪B)=P(A)+P(B)-P(A∩B)
=0.25+0.50-0.14=0.61
P(A'∪B') =1-0.61=0.39

Q2.The probability of India winning a test match against West-Indies is 1/2 assuming independence from match to match the probability that in a match series India’s second win occurs at the third test, is
•  1/8
•  1/4
•  1/2
•  2/3
Solution
(b) Required probability P(A1∩A'2∩A3 )+P(A'1∩A2∩A3 ) =P(A1 )P(A'2 )P(A3 )+P(A'1 )P(A2)P(A3) =(1/2)3+(1/2)3 =1/8+1/8=1/4
Q3.  The mean and variance of binomial distribution are 4 and 3 respectively. Then, the probability of getting exactly six success in this distribution is
•   16C6 (1/4)6 (3/4)10
•  16C6 (1/4)6 (3/4)20
•  16C6 (1/4)8 (3/4)12
•  16C6 (1/4)16 (3/4)20
Solution
(a) Given, np=4,npq=3 ⇒ P=1/4,q=3/4
∴ P(X=6)=16C6 (1/4)6.(3/4)10

Q4. If m and
Ïƒ2 are the mean and variance of the random variable X. whose distribution is given by
then
•  m=Ïƒ2=2
•  m=1,Ïƒ2=2
•  m=Ïƒ2=1
•  m=2,Ïƒ2=1
Solution

Q5.Let A={1,3,5,7,9},B={2,4,6,8}. If a cartesian product A×B, if chosen at random, the probability of a+b=9 is
•  1/4
•  1/5
•  1
•  0
Solution
(b) Total number of cases=20
Favorable cases={(1,8),(3,6),(5,4),(7,2)}=4
∴ Required probability =4/20=1/5

Q6. If two dice are thrown simultaneously, then probability that 1 comes on first dice, is
•   1/36
•  5/36
• 1/6
•   None of these
Solution
(c) 1/6

Q7.A bag contains 4 tickets numbered 1,2,3,4 and another bag contains 6 tickets numbered 2,4,6,7,8,9. One bag is chosen and a ticket is drawn. The probability that the ticket bears the number 4 is
•  1/48
•  1/8
•  5/24
•  None of these
Solution
(c) Consider the following events:
E1= Selecting first bag
E2= Selecting second bag A= Getting a ticket bearing number 4
∴ Required probability =P((E1∩A)∪(E2∩A)) =P(E1∩A)+P(E2∩A) =P(E1)P(A/E1 )+P(E2 )P(A/E2) =1/2×1/4+1/2×1/6=5/24

Q8.A pair of a dice thrown, if 5. appears on at least one of the dice, then the probability that the sum is 10 or greater, is
•  11/36
•  2/9
•  3/11
•  1/12
Solution
(d) Favourable cases of getting 10 or greater than 10, if 5 appears on atleast one of dice. ={(5,6),(6,5),(5,5)}
Number of favourable cases =3 Total number of cases = 36
∴ Required probability =3/36=1/12

Q9.Probability of all 3 digit numbers having all the digits same is
•  1/100
•  3/100
•  7/100
•  None of these
Solution
(a) There are 9 favourable cases in which all three digits are same.
∴Required probability=9/900=1/100

Q10. If the probability of A to fail in an examination is 0.2 and that for B is 0.3, then probability that either A or B is fail, is
•  0.5
•  0.44
•  0.8
• 0.25
Solution
(b) Here, A and B are independent events
∴ P(A∩B)=P(A).P(B)=0.06 Now, P(A∪B)=P(A)+P(B)-P(A∩B) =0.2+0.3-0.06=0.44

#### Written by: AUTHORNAME

AUTHORDESCRIPTION

## Want to know more

Please fill in the details below:

## Latest NEET Articles\$type=three\$c=3\$author=hide\$comment=hide\$rm=hide\$date=hide\$snippet=hide

Name

ltr
item
BEST NEET COACHING CENTER | BEST IIT JEE COACHING INSTITUTE | BEST NEET & IIT JEE COACHING: Probability-quiz-1
Probability-quiz-1
BEST NEET COACHING CENTER | BEST IIT JEE COACHING INSTITUTE | BEST NEET & IIT JEE COACHING
https://www.cleariitmedical.com/2020/10/probability-quiz-1.html
https://www.cleariitmedical.com/
https://www.cleariitmedical.com/
https://www.cleariitmedical.com/2020/10/probability-quiz-1.html
true
7783647550433378923
UTF-8