A die thrown three times,E : 4 appears on the third toss,F : 6

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 Multiple Choice QuestionsShort Answer Type

751. A die is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?
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752.

A die is thrown and the sum of the numbers appearing is observed to be 7. What is the conditional probability that the number 2 has appeared at least once. 

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753. A pair of fair dice is thrown. Find the probability that the sum is 10 or greater if 5 appears on the first die.
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754.

Find the probability that a single throw of a die results in a number less than 6 if
(i) no other information is given
(ii) it is given that the throw resulted in an odd number

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755.

A pair of dice is thrown . If the sum is seven, find the probability that one of the dice shows 3.

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756. One card is drawn from a well shuffled pack of 52 cards. If E is the event “the card drawn is a king or queen” and F is the event “the card drawn is a queen or an ace”, then find the probability of the conditional event E/F.
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757. A bag contains 3 red and 7 black balls. Two balls are selected at random without replacement. If the second selected is given to be red. what is the probability that the first selected is also red?
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758. A bag contains 3 red and 7 black balls. Two balls are selected at random with replacement. If the second selected is given to be red, what is the probability that the first selected is also red?
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759.

A die thrown three times,
E : 4 appears on the third toss,
F : 6 and 5 appears respectively on First two tosses
Determine P(E | F).


Here a die is thrown three times
 therefore  sample space has 6 x 6 x 6 = 216 outcomes.
therefore space space space straight E space equals space open curly brackets table row cell left parenthesis 1 comma space 1 comma space 4 right parenthesis end cell cell left parenthesis 1 comma space 2 comma space 4 right parenthesis... end cell cell left parenthesis 1 comma space 6 comma space 4 right parenthesis end cell cell left parenthesis 2 comma space 1 comma space 4 right parenthesis end cell cell left parenthesis 2 comma space 2 comma space 4 right parenthesis... end cell cell left parenthesis 2 comma space 6 comma space 4 right parenthesis end cell row cell left parenthesis 3 comma space 1 comma space 4 right parenthesis end cell cell left parenthesis 3 comma space 2 comma space 4 right parenthesis... end cell cell left parenthesis 3 comma space 6 comma space 4 right parenthesis end cell cell left parenthesis 4 comma space 1 comma space 4 right parenthesis end cell cell left parenthesis 4 comma space 2 comma space 4 right parenthesis... end cell cell left parenthesis 4 comma space 6 comma space 4 right parenthesis end cell row cell left parenthesis 5 comma space 1 comma space 4 right parenthesis end cell cell left parenthesis 5 comma space 2 comma space 4 right parenthesis... end cell cell left parenthesis 5 comma space 6 comma space 4 right parenthesis end cell cell left parenthesis 6 comma space 1 comma space 4 right parenthesis end cell cell left parenthesis 6 comma space 2 comma space 4 right parenthesis... end cell cell left parenthesis 6 comma space 6 comma space 4 right parenthesis end cell end table close curly brackets
       F: 6 and 5 appear respectively on first two tosses
therefore space space space space straight F space equals space open curly brackets left parenthesis 6 comma space 5 comma space 1 right parenthesis thin space left parenthesis 6 comma space 5 comma space 2 right parenthesis comma space left parenthesis 6 comma space 5 comma space 3 right parenthesis comma space left parenthesis 6 comma space 5 comma space 4 right parenthesis comma space left parenthesis 6 comma space 5 comma space 5 right parenthesis comma space left parenthesis 6 comma space 5 comma space 6 right parenthesis close curly brackets
      straight E intersection straight F space equals space open curly brackets left parenthesis 6 comma space 5 comma space 4 right parenthesis close curly brackets
Now,  
          straight P left parenthesis straight F right parenthesis space equals space 6 over 216 comma space space straight P left parenthesis straight E intersection straight F right parenthesis space equals space 1 over 216
   therefore space space space straight P left parenthesis straight E space left enclose straight F right parenthesis space equals space fraction numerator straight P left parenthesis straight E space intersection space straight F right parenthesis over denominator straight P left parenthesis straight F right parenthesis end fraction space equals fraction numerator begin display style 1 over 216 end style over denominator begin display style 6 over 216 end style end fraction space equals 1 over 6
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760.

A coin is tossed three times, where
E : head on third toss,     F : heads on first two tosses

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