## Jagat Chaudhary is teaching live on Unacademy Plus

IIT-JEE (main +Advanced) Probability On

Equally likely Events:

Equally likely Events: Events are said to be equally likely, when No particular event has a preference to occur in relation to other event.

Equally likely Events: Events are said to be equally likely, whe particular event has a preference to occur in relation to othe event. Example: Experiment is Dice is rolled. E1: Getting face 1 then P(E1)-1/6 E2: Getting face 2 then P(E2)-1/6

Equally likely Events: Events are said to be equally likely, when No particular event has a preference to occur in relation to other event. Example: Experiment is Dice is rolled. E1: Getting face 1 then P(E1)-1/6 E2: Getting face 2 then P(E2)-1/6 Then E1 and E2 are equally likely

Equally likely Events: Events are said to be equally likely, when No particular event has a preference to occur in relation to other event. Example: Experiment is Dice is rolled. E1: Getting face 1 then P(E1)-1/6 E2: Getting face 2 then P(E2)-1/6 Then E1 and E2 are equally likely Mutuallv Exclusive Events;

Equally likely Events: Events are said to be equally likely, when No particular event has a preference to occur in relation to other event. Example: Experiment is Dice is rolled. E1: Getting face 1 then P(E1)-1/6 E2: Getting face 2 then P(E2)-1/6 Then E1 and E2 are equally likely Mutually Exclusive Events:Events are said to be mutually excusive, if their Simultaneous occurrence is impossible.

Equally likely Events: Events are said to be equally likely, when No particular event has a preference to occur in relation to other event Example: Experiment is Dice is rolled. E1: Getting face 1 then P(E1)-1/6 E2: Getting face 2 then P(E2)-1/6 Then E1 and E2 are equally likely Mutually Exclusive Events:Events are said to be mutually excusive, if their Simultaneous occurrence is impossible. Example: E,: Throwing a total of 7 when two Different Dice are rolled. E2 : Throwing a total of 11when two Different Dice are rolled.

Example: Experiment is Dice is rolled. E1: Getting face 1 then P(E1)-1/6 E2: Getting face 2 then P(E2)-1/6 Then E1 and E2 are equally likely Mutually Exclusive Events: Events are said to be mutually excusive, i their Simultaneous occurrence is impossible. Example E1: Throwing a total of 7 when two Different Dice are rolled. E2 Throwing a total of 11when two Different Dice are rolled. Yes these are mutually exclusive.

particular event has a preference to occur in relation to other event. Example: Experiment is Dice is rolled. E1: Getting face 1 then P(E1)-1/6 E2: Getting face 2 then P(E2)-1/6 Then E1 and E2 are equally likely Mutually Exclusive Events: Events are said to be mutually excusive, if their Simultaneous occurance is impossible Example E1: Throwing a total of 7 when two Different Dice are rolled. E2 : Throwing a total of 11when two Different Dice are rolled. Yes these are mutually exclusive. A : Getting a doublet B: Sum is 10

Equally likely Events: Events are said to be equally likely, when No particular event has a preference to occur in relation to other event. Example: Experiment is Dice is rolled. E1: Getting face 1 then P(E1)-1/6 E2: Getting face 2 then P(E2)-1/6 Then E1 and E2 are equally likely Mutually Exclusive Events: Events are said to be mutually excusive, if their Simultaneous occurance is impossible. Example:E1: Throwing a total of 7 when two Different Dice are rolled. E2 Throwing a total of 11when two Different Dice are rolled. Yes these are mutually exclusive. A : Getting a doublet B: Sum is 10 This is not mutually exclusive

Mutually exclusive / disjoint/ incompatible events: Two events are said to be mutually exclusive if occurrence of one of them rejects the possibility o occurrence of the other i.e. both cannot occur simultaneously. In the vein diagram the events A and B are mutually exclusive. Mathematically, we write Events A1, A2, , A"n are said to be mutually exclusive events iff AinA=ovi, j e {1, 2, , n} where i # j

Mutually Exhaustive events: Event as a consequence of an experimental perforamance are said to be exhaustive if nothing beyond those listed in the set of Possible outcomes/ Sample space can occur.

General Points:

General Points: 1. Probability of a sure event is 1 Example: Probability of getting either head or tail whena coin is tossed 2. Probability of an impossible event is zero.

General Points: 1. Probability of a sure event is 1 Example: Probability of getting either head or tail when a coin is tossed 2. Probability of an impossible event is zero. Example Probability of getting 6 when a coin is tossed.

General Points: 1. Probability of a sure event is 1 Example: Probability of getting either head or tail when a co tossed 2. Probability of an impossible event is zero Example Probability of getting 6 when a coin is tossed. 3. Consider two events A and B which are mutually exclusive occurrence of both simultaneously is Impossible.

General Points: 1. Probability of a sure event is 1 Example: Probability of getting either head or tail when a co tossed 2. Probability of an impossible event is zero Example Probability of getting 6 when a coin is tossed 3. Consider two events A and B which are mutually exclusive occurrence of both simultaneously is Impossible. Then probability is zero because n(ATB)-O 4. A and B are exhaustive defined on a sample space then

General Points; 1. Probability of a sure event is 1 Example: Probability of getting either head or tail when a co tossed 2. Probability of an impossible event is zero Example Probability of getting 6 when a coin is tossed 3. Consider two events A and B which are mutually exclusive occurrence of both simultaneously is Impossible. Then probability is zero because n(ANB)-O 4. A and B are exhaustive defined on a sample space then P(AUB)-1

Addition theorem of probability:

Addition theorem of probability: If 'A' and 'B' are any two events associated with an experiment, then P(AuB) P(A) P(B) P(AnB) De Morgan's laws : If A & B are two subsets of a universal set U, then

Ques: An old man while dialing a seven digit phone number. After having dialed the first 5 digits, suddenly forgets the last two but he remembered that the last two digits were different. What is the probability that Correct phone number will be dialed

Ques: An old man while dialing a seven digit phone number. After having dialed the first 5 digits, suddenly forgets the last two but he remembered that the last two digits were different. What is the probability that Correct phone number will be dialed Sol: We have to check possibility for last two digits

Ques: An old man while dialing a seven digit phone number. After having dialed the first 5 digits, suddenly forgets the last two but he remembered that the last two digits were different. What is the probability that Correct phone number will be dialed Sol: We have to check possibility for last two digits total possible outcomes or Sample space have n(S)-10x9-90

Ques: An old man while dialing a seven digit phone number. After having dialed the first 5 digits, suddenly forgets the last two but he remembered that the last two digits were different. What is the probability that Correct phone number will be dialed Sol: We have to check possibility for last two digits total possible outcomes or Sample space have n(S)-10x9-90 Correct outcomes n(A)-1 hence P(A)- n(S)

Ques: An old man while dialing a seven digit phone number. After having dialed the first 5 digits, suddenly forgets the last two but he remembered that the last two digits were different. What is the probability that Correct phone number will be dialed. Sol: We have to check possibility for last two digits total possible outcomes or Sample space have n(S)-10x9-90 Correct outcomes n(A)-1 hence P(A))1 n(S) 90