JEE Main 2013 (Offline) | Probability Question 173 | Mathematics

A multiple choice examination has $$5$$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $$4$$ or more correct answers just by guessing is :

$${{17} \over {{3^5}}}$$

$${{13} \over {{3^5}}}$$

$${{11} \over {{3^5}}}$$

$${{10} \over {{3^5}}}$$

AIEEE 2012

MCQ (Single Correct Answer)

-1

Three numbers are chosen at random without replacement from $$\left\{ {1,2,3,..8} \right\}.$$ The probability that their minimum is $$3,$$ given that their maximum is $$6,$$ is :

$${3 \over 8}$$

$${1 \over 5}$$

$${1 \over 4}$$

$${2 \over 5}$$

AIEEE 2011

MCQ (Single Correct Answer)

-1

Out of Syllabus

Consider $$5$$ independent Bernoulli's trials each with probability of success $$p.$$ If the probability of at least one failure is greater than or equal to $${{31} \over 32},$$ then $$p$$ lies in the interval :

$$\left( {{3 \over 4},{{11} \over {12}}} \right]$$

$$\left[ {0,{1 \over 2}} \right]$$

$$\left( {{11 \over 12},1} \right]$$

$$\left( {{1 \over 2},{{3} \over {4}}} \right]$$

AIEEE 2011

MCQ (Single Correct Answer)

-1

If $$C$$ and $$D$$ are two events such that $$C \subset D$$ and $$P\left( D \right) \ne 0,$$ then the correct statement among the following is :

$$P\left( {{C \over D}} \right)$$$$ \ge P\left( C \right)$$

$$P\left( {{C \over D}} \right)$$$$ < P\left( C \right)$$

$$P\left( {{C \over D}} \right)$$$$ = {{P\left( D \right)} \over {P\left( C \right)}}$$

$$P\left( {{C \over D}} \right)$$$$ = P\left( C \right)$$