Statistics and Probability Answers

There are 7 English, 5 Marathi and 4 Hindi Books. In how many ways can they be arranged in a shelf such that,

(i) the books are language wise.

(ii) the books are not language wise strictly, although some but not all books of same
language may be together.

Interviews are being conducted for two posts at same level in a company. There are 3 female and 5 male candidates. In how many ways can the candidates be selected such that

(i) Both posts are filled by males

(ii) Both posts are filled by females

(iii) One male and one female get selected?

(a) A group of 5 boys and 4 girls are to be photographed. In how many ways can they be arranged such that:

(i) No two girls sit together?

(ii) No two boys sit together?

The I . Q . of students of a school was found to be normally distributed with a mean µ = 116 and a standard deviation of σ = 8 . What % age of children have I . Q . fr om 100 to 124 .

In how many ways the letters of the word ‘FARIDABAD’ can be arranged so that there are no repetitions .

At a particular restaurant, 63% of all customers order an appetizer and 40% of all customers order dessert. If 76% of all customers order an appetizer or dessert (or both), what is the probability a randomly selected customer orders both an appetizer and dessert?

Use Venn diagram to illustrate the following problem :

In a college out of the 100 students, in all 40 students p lay cricket; 15 play cricket and volleyball and 17 play only cricket . 14 students play only volleyball; 10 play volleyball and hockey ; 4 students play all 3 games and 12 play only hockey . Remaining do not play any game .

(i) H ow many students do not p lay any game?
(ii) In all how many students play hockey?

In how many ways the letters of the word ‘BANGALORE’ can be arranged so that there are no repetitions.

In a certain school, the students engage in various sports in the following
proportions:
Cricket (C) : 60% of all students
Tennis (T) : 50% of all students
Both Cricket & Tennis : 30% of all students
If a student is selected at random, what is the probability that he will
(i) Play Cricket or Tennis
(ii) Play neither sports?

The odds that X speaks the truth are 3:2 and the odds that Y speaks the truth are 5:3. In what percentage of the cases are they likely to contradict each other?