Question

there are 37 students in a class one of them being the monitor and 37 seats in the classroom everyday 37 students line up in a random order and then enter the classroom one by one except for the monitor each student will randomly choose an unoccupied seat and sit down the monitor however preferred the seat next to the door and chooses if it's possible let p upon 37 be the probability that the monitor can have a favourite seat find p​

Answer 1

Given : there are 37 students in a class one of them being the monitor and 37 seats in the classroom everyday 37 students line up in a random order and then enter the classroom one by one except for the monitor each student will randomly choose an unoccupied seat and sit down the monitor however preferred the seat next to the door and chooses if it's possible let p upon 37 be the probability that the monitor can have a favorite seat

To find : p​

Solution:

Chances of monitor being at each position from 1 st to 37 each is 1/37

If Monitor is at 1st position then chances to choose seat = (1/37) * 1

if Monitor is at 2nd position then (1/37) ( ³⁶C₁/³⁷C₁)

as 1 student ahead of him can choose 1 position in 37 ways  and monitor gets his preferred seat if they choose one out of remaining 36 )

if Monitor is at 3rd  position then (1/37) ( ³⁶C₂/³⁷C₂)

and so on  till     ( 1/37) ( ³⁶C₃₆/³⁷C₃₆)

Hence probability =

(1/37) ( 1 +  ³⁶C₁/³⁷C₁  + ³⁶C₂/³⁷C₂ + _________ + ³⁶C₃₅/³⁷C₃₅ + ³⁶C₃₆/³⁷C₃₆)

as probability is p/37

Hence

p = 1 +  ³⁶C₁/³⁷C₁  + ³⁶C₂/³⁷C₂ + _________ + ³⁶C₃₅/³⁷C₃₅ + ³⁶C₃₆/³⁷C₃₆

=37/37 +  36/37  + 35/37  + 34/37  + _________ + 2/37  + 1/37

= ( 1/37)( 37 + 36 + 35 +  _________ 2 + 1)

= (1/37) ( 37 * 38 / 2)

=  19

Value of p is  19

Learn More:

An urn contains 8 balls : 4 red , 2 blue and 2 green. Now n balls are ...

brainly.in/question/14735198

X is a binomial variable such that 2 P(X = 2) = P(X = 3) and mean

brainly.in/question/17528101

the probability that man is 45 years will die within a year is 0.012 ...

brainly.in/question/19206650