Help me solve these...?

Question

1)What is the probablility that there wil be 53 sundays in a randomly selected :

a)Leap year

b)Non-leap year

2)A university has a total of 320 professors & 105 of them are women... Whats the probability that a randomly selected professor from the Univ is

a) A woman

b) man

Answer 1

2) Ans.  Total no. of professor is 320 and 105 of them are women.Hence the no. of man is (320-105)=115

then the probability for random chosen will be a women is 105/320.

and prob.of a man is 115/320.

Answer 2

Leap year  53 sundays

non leap year 52 sundays

0.32 woman

0.67man

Answer 3

1) Leap year has 366 days = 52*7 + 2 ,

it means to have 53 Sundays the year should get started from sunday or saturday. Taking the equal probability starting year, probability is 2/7

Non-leap year has 365 days =52*7 + 1 this time the year should get started just from Sunday? the probability is 1/7

2)The probability (it's a woman) is 105/320= 21/64

(it's a man is1-21/64=43/64

Answer 4

1) a 0

    b) 0

2) how many g*y professors r thr in university

Answer 5

1)

a)  Leap year has 52 weeks (365/7) + 2 extra days ie.   52 Sundays + 2 day which can be any of the seven days. So probability of 53 Sundays === Probability of any one of those 2 days being a sunday

Possible options are Mon/Tue ;Tue/Wed ;Wed/Thu ;Thu/Fri ;Fri/Sat ; Sat/Sun and Sun/Mon. Two possible options have a Sunday. So probability = 2/7

b) Normal year has 52 weeks (365/7) + 1 extra day ie. 52   Sundays + 1 day which can be any of the seven days So probability of 53 Sundays === Probability of that day being a sunday = 1/7

2) 320 professors. 105 of then are women.

So rest are men.   Thus, 215 male professors.

Probability of a randomly selected Prof. being a -:

a) woman = 105 / 320 = 0.328125

b) man     = 215 / 320 = 0.671875