1993 HSC harder probability question (1 Viewer)

[hermine]

el annoyance that it probably is an easy question, thanks in advance

In the next 7 days, called day 1, day 2, ... , day 7, Esther and George must each take 3 days in a row off work. They choose their consecutive 3 days randomly and independently of each other.

i. Show that the probability that they both have day 1 off together is 1/25
I use 5C1x5C1=25 but 1/25?

ii. What is the probability that day 2 is the first day that they both have off together?

iii. Find the probability that Esther and George have at least one day off together



answers
ii) 3/25
iii)19/25

 

[Timothy.Siu]

el annoyance that it probably is an easy question, thanks in advance

In the next 7 days, called day 1, day 2, ... , day 7, Esther and George must each take 3 days in a row off work. They choose their consecutive 3 days randomly and independently of each other.

i. Show that the probability that they both have day 1 off together is 1/25
I use 5C1x5C1=25 but 1/25?

ii. What is the probability that day 2 is the first day that they both have off together?

iii. Find the probability that Esther and George have at least one day off together



answers
ii) 3/25
iii)19/25

i)1/5x1/5 the probability of them choosing the day 1 is 1/5
ii)just take cases, either they both take their first day off on day 2, or one takes days off on the first day and the second one takes them on the 2nd day.
so, 1/5x1/5+1/5x1/5+1/5x1/5
iii)i guess u can just take cases....
3/25+4/25+5/25+4/25+3/25
i just did every case.
i.e. first day prob. 1/5 , then 3/5 chance of getting at least one day
2nd day as first day off, 1/5 then 4/5 chance...
etc.

 

[hermine]

iii)i guess u can just take cases....
3/25+4/25+5/25+4/25+3/25
i just did every case.
i.e. first day prob. 1/5 , then 3/5 chance of getting at least one day
2nd day as first day off, 1/5 then 4/5 chance...
etc.

I dont understand how you got the probs of the cases

 

[Timothy.Siu]

just did 1/5x3/5
taking the case that some guy got leave on the first day
thats 1/5, and the chance for the other person to have have leave on the same day is 3/5, since he can take the 3 days off on either day 1,2 or 3.

similarly for the rest.