Question

a) Find the probability that a leap year, selected at random will have 53 sundays
b) A bag contains 10 white balls and x black balls. If the probability of drawing a black ball is double that of a white ball, find X
c) In a sample of 500 items, 120 are found to be defective. Find the probability that the item selected at random is
(i) defective
(ii) non-defective

Answer 1

A) a leap year has 366 days it means 52 weeks(52 sundays) and 2 odd days.
     then, 2 days may be
     sunday and monday
     monday and tuesday
     tuesday and wednesday
     wednesday and thursday
     thursday and friday
     friday and saturday
     saturday and sunday
probability of 53 sundays = no.of sundays
                                       total days
                                     = 2
                                        7
(b) Total balls=black balls +white balls
                    x+10
 p(drawing black balls)=2 p(drawing  white balls)
    x                           =2 10    
    x+10                           x+10
x=20 black balls

(c) {i}   p(defective balls)=120
                                      500
                                    =0.24
    {ii}   p(non defective balls)=1- 120
                                               500
                                          =0.76