Probability,Set theory - discussions,Q & A


This is about probability and Set theory the section.Every year you will find a 2 marks question from probability/Sets. Do all the discussion related to probability/Sets here.


Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday
to Saturday). Each is equally likely to visit the shop on any day as on another day. What
is the probability that both will visit the shop on (i) the same day? (ii) consecutive
days? (iii) different days?


A die is numbered in such a way that its faces show the numbers 1, 2, 2, 3, 3, 6. It is
thrown two times and the total score in two throws is noted.What is the probability that the total score is
(i) even?
(ii) 6?
(iii) at least 6?


(i). The score will be even if either both dice show even no. or both show odd no. since there are 3 instance of odd no. (1, 3, ,3) and 3 (2, 2 6) for even no. So no. of favorable outcomes will be 2* (3 * 3 ) = 18.
Total possible outcomes = 6 * 6 = 36.

so probability will be 18/36 = 1/2 .

(ii) The score will be 6 is either of dices show 3. since each dice marked 3 twice in its face. so there will be total for favorable outcomes 2 * 2.
probability = 4 / 36 = 1/9
(iii) for this sum could be 6 or 9. since there are 4 cases which give sum as 9 (explained in (ii)). for 9 there will be 2 cases - (3, 6) , (6, 3).
probability = 4+ 2 / 36 = 1/6


Question) P and Q are considering to apply for a job. The probability that P applies for the job is 1/4, the probability that P applies for the job given that Q applies for the job is 1/2., and the probability that Q applies for the job given that P applies for the job is 1/3. Then the probability that P does not apply for the job given that Q does not apply for this job is

a) 4/5
b) 5/6
d) 11/12


Among 150 faculty members in an institute, 55 are connected with each other through Facebook and 85 are connected through WhatsApp . 30 faculty members do not have Facebook or WhatsApp accounts. The number of faculty members connected only through Facebook accounts is


Now this is a typical set theory problem just a little attention needed.

First of all we will try to solve it using just intuition no formula or anything.Since there are 30 faculty members who dont like facebook and whatsapp,we are left with 150 - 30 = 120 members.
Now if you will add 55 + 85 = 140 there coming 20 extra members,from where these extra members coming.
Now this is the crux of these type of questions ,beacause when there are people who like 2 things like here there are some persons who use both facebook and whatsapp,the problem with these members is that we count them twice,so for example there 3 who use only facebook,3 who only whatsapp and 1 who use both facebook and whatsapp,now how will the question be framed here,we will say there 4 who use facebook ,4 who use whatsapp and 1 who do both,dat will add to 8 members,but actually number of members are only 7 since we have counted the person who uses both facebook and whatsapp twice,so we need to subtract it once(we still have to count it,cant subtract two times),so 140 - 120 = 20 uses both facebook and whatsapp,so the number of faculty members who uses only facebook is 55 - 20 = 35.

Bonus:Can you imagine the situation with three groups like some uses facebook,some whatsapp,some uses snapchat.How do we solve those questions by intuition and basic thinking.