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Probability

Short Answer Type

761.

A coin is tossed three times, where
E : at least two heads , F : at most two heads

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762.
A coin is tossed three times, where
E : at most two tails , F : at least one tail

Here S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
E: at most two tails
$therefore space space straight E space equals space open curly brackets HHH comma space HHT comma space HTH comma space THH comma space TTH comma space THT comma space HTT close curly brackets$
F: at least one tail
$therefore space space space straight F space equals space open curly brackets HHT comma space HTH comma space THH comma space TTH comma space THT comma space HTT comma space TTT close curly brackets therefore space space space space straight E space intersection thin space straight F space equals space open curly brackets HHT comma space HTH comma space THH comma space TTH comma space THT comma space HTT close curly brackets therefore space space space straight P left parenthesis straight E right parenthesis space equals space 7 over 8 comma space space space straight P left parenthesis straight F right parenthesis space equals space 7 over 8 comma space space straight P left parenthesis straight E intersection straight F right parenthesis space equals space 6 over 8 space equals 3 over 4 therefore space space space space straight P left parenthesis straight E space left enclose straight F right parenthesis space space equals space fraction numerator straight P left parenthesis straight E intersection straight F right parenthesis over denominator straight P left parenthesis straight F right parenthesis end fraction space equals fraction numerator begin display style 6 over 8 end style over denominator begin display style 7 over 8 end style end fraction space equals space 6 over 7.$

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763. A black and a red dice are rolled.Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.

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764. A black and a red dice are rolled. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

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Long Answer Type

765. Given that the two numbers appearing on throwing two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.

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766. 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. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?

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Short Answer Type

767. Find the probability of drawing a king, when a card is drawn from a well shuffled pack of cards. It is also given that the card drawn is a face card.

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768.

Two coins are tossed once, where
E : tail appears on one coin, F : one coin shows head
Determine P(E | F).

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769.

Two coins are tossed once, where
E : no tail appears, F : no head appears
Determine P(E | F).

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770. Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that the youngest is a girl?

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