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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

85 Views

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.

Here $straight S space equals space open curly brackets table row cell left parenthesis 1 comma space 1 right parenthesis end cell cell left parenthesis 1 comma space 2 right parenthesis end cell cell left parenthesis 1 comma space 3 right parenthesis end cell cell left parenthesis 1 comma space 4 right parenthesis end cell cell left parenthesis 1 comma space 5 right parenthesis end cell cell left parenthesis 1 comma space 6 right parenthesis end cell row cell left parenthesis 2 comma space 1 right parenthesis end cell cell left parenthesis 2 comma space 2 right parenthesis end cell cell left parenthesis 2 comma space 3 right parenthesis end cell cell left parenthesis 2 comma space 4 right parenthesis end cell cell left parenthesis 2 comma space 5 right parenthesis end cell cell left parenthesis 2 comma space 6 right parenthesis end cell row cell left parenthesis 3 comma space 1 right parenthesis end cell cell left parenthesis 3 comma space 2 right parenthesis end cell cell left parenthesis 3 comma space 3 right parenthesis end cell cell left parenthesis 3 comma space 4 right parenthesis end cell cell left parenthesis 3 comma space 5 right parenthesis end cell cell left parenthesis 3 comma space 6 right parenthesis end cell row cell left parenthesis 4 comma space 1 right parenthesis end cell cell left parenthesis 4 comma space 2 right parenthesis end cell cell left parenthesis 4 comma space 3 right parenthesis end cell cell left parenthesis 4 comma space 4 right parenthesis end cell cell left parenthesis 4 comma space 5 right parenthesis end cell cell left parenthesis 4 comma space 6 right parenthesis end cell row cell left parenthesis 5 comma space 1 right parenthesis end cell cell left parenthesis 5 comma space 2 right parenthesis end cell cell left parenthesis 5 comma space 3 right parenthesis end cell cell left parenthesis 5 comma space 4 right parenthesis end cell cell left parenthesis 5 comma space 5 right parenthesis end cell cell left parenthesis 5 comma space 6 right parenthesis end cell row cell left parenthesis 6 comma space 1 right parenthesis end cell cell left parenthesis 6 comma space 2 right parenthesis end cell cell left parenthesis 6 comma space 3 right parenthesis end cell cell left parenthesis 6 comma space 4 right parenthesis end cell cell left parenthesis 6 comma space 5 right parenthesis end cell cell left parenthesis 6 comma space 6 right parenthesis end cell end table close curly brackets$
Number of elements (outcomes) of the above sample space is 6 × 6 = 36.
Let E : sum greater than 9
$therefore space space space straight E space equals space open curly brackets left parenthesis 4 comma space 6 right parenthesis comma space left parenthesis 5 comma space 5 right parenthesis comma space left parenthesis 5 comma space 6 right parenthesis comma space left parenthesis 6 comma space 4 right parenthesis comma space left parenthesis 6 comma space 5 right parenthesis comma space left parenthesis 6 comma space 6 right parenthesis close curly brackets$
Let E: black dice resultant in a 5.
$therefore space space space space straight F thin space colon thin space open curly brackets left parenthesis 5 comma space 1 right parenthesis comma space left parenthesis 5 comma space 2 right parenthesis comma space left parenthesis 5 comma space 3 right parenthesis comma space left parenthesis 5 comma space 4 right parenthesis comma space left parenthesis 5 comma space 5 right parenthesis comma space left parenthesis 5 comma space 6 right parenthesis close curly brackets$
$straight E space intersection thin space straight F space equals space open curly brackets left parenthesis 5 comma space 5 right parenthesis comma space left parenthesis 5 comma space 6 right parenthesis close curly brackets$
$therefore space space space space straight P left parenthesis straight F right parenthesis space equals space 6 over 36 comma space space space space straight P left parenthesis straight E intersection straight F right parenthesis space equals space 2 over 36$
Required probability = $straight P left parenthesis straight E left enclose straight F right parenthesis end enclose space equals space fraction numerator straight P left parenthesis straight E intersection straight F right parenthesis over denominator straight P left parenthesis straight F right parenthesis end fraction space equals fraction numerator begin display style 2 over 36 end style over denominator begin display style 6 over 36 end style end fraction space equals space 2 over 6 space equals space 1 third.$

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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.

169 Views

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’.

142 Views

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?

173 Views

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.

222 Views

768.

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

82 Views

769.

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

80 Views

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?

104 Views