ADMISSION-Short Placement Tests Developed by ACT Set 2

If P (n-1, 3): P (n, 3) = 1:9, find n.

In how many ways can 9 students be seated in a row such that the tallest child and the shortest child never sit together?

There are three events A, B and C one of which must happen. At a time only one can happen. The odds are 8 to 3 against A, 5 to 2 against B , find the odds against C

One of two events must happen. Given that the chance of one is two-third of the other, find the odds in favour of the other.

In a class the probability of all the students passing the mathematics examination is 0.8 that of the whole class passing the Hindi examination is 0.7. If the probability of the whole class passing in at least one of the two exams is 0.95, then find the probability of not getting any failures in the whole class in both mathematics and Hindi.

In an entrance test that is graded on the basis of English and general knowledge, the probability of a randomly chosen student passing both the tests is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English test is 0.75, then what is the probability of passing the general knowledge test?

In a lottery of 50 tickets numbered 1 to 50, two tickets are drawn simultaneously. Find the odds in favor that none of the tickets has a prime number.

There are 9 letters; 5 consonants and 4 vowels. Three letters are chosen at random. What is the probability of choosing more than one vowel?

A bag contains 50 tickets numbered 51,52,...,100 of which 5 are drawn and arranged in ascending order of magnitude. Find the probability that the third number is 80.

Four persons are to be chosen from a group of 3 men, 2 women and 4 children. Find the probability of choosing exactly 2 women.