Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin.
Total outcomes
Total number of outcomes =20
Let A be a event when coin shows a tail.
Let B be a event that ‘at least one die shows a 3’.

Two dice are thrown.
Total outcomes
Let A be the event ‘the sum of numbers on the dice is 4.
Let B be the event that two numbers appearing on throwing two dice are different.
Therefore, the required probability is 1/15

An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions.
Total number of questions
Let A = question be easy.
Let B = multiple choice question
easy multiple questions
Therefore, the required probability is 5/9

Assume that each born child is equally likely to be a boy or a girl.
Let first and second girl are denoted by respectively also first and second boy are denoted by
If a family has two children, then total outcomes
Let A= both are girls
and C= at least one is a girl =

Assume that each born child is equally likely to be a boy or a girl.
Let first and second girl are denoted by respectively also first and second boy are denoted by
If a family has two children, then total outcomes
Let A= both are girls
and B= the youngest is a girl =
Therefore, the required probability is 1/2

A black and a red dice are rolled.
Total outcomes
Let the A be event obtaining a sum 8 and B be a event thatthat the red die resulted in a number less than .
Red dice is rolled after black dice.

A black and a red dice are rolled.
Total outcomes
Let the A be event obtaining a sum greater than and B be a event that the black die resulted in a

E : son on one end, F : father in middle
Total outcomes
Let S be son, M be mother and F be father.
Then we have,

E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses
Total outcomes

The sample space S when a coin is tossed three times is
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
It can be seen that the sample space (S) has 8 elements.
Total number of outcomes
According to question
E: at most two tails, F: at least one tail

The sample space S when a coin is tossed three times is
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
It can be seen that the sample space (S) has 8 elements.
Total number of outcomes
According to question
E : at least two heads , F : at most two heads

**Q. 6. ** A coin is tossed three times, where

(i) E : head on third toss , F : heads on first two tosses

The sample space S when a coin is tossed three times is
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
It can be seen that the sample space (S) has 8 elements.
Total number of outcomes
According to question
E: head on third toss, F: heads on first two tosses

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