A bag contains 3 red and 7 black balls. Two balls are selected a

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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?


Let R1, R2 be the events that red ball is drawn in the first and second draw. Here balls are drawn without replacement.
 therefore space space space straight P left parenthesis straight R subscript 1 space space intersection space straight R subscript 2 right parenthesis space equals space straight P left parenthesis both space red space balls right parenthesis space equals space 3 over 10 cross times 2 over 9 space equals 1 over 15

straight P left parenthesis straight R subscript 2 right parenthesis space equals space straight P left parenthesis apostrophe straight R subscript 1 straight R subscript 2 apostrophe space or space space apostrophe BR subscript 2 apostrophe right parenthesis space equals space straight P left parenthesis straight R subscript 1 space straight R subscript 2 right parenthesis space plus space straight P left parenthesis BR subscript 2 right parenthesis
space space space space space space space space space space space equals space 3 over 10 cross times 2 over 9 plus 7 over 10 cross times 3 over 9 space equals space 6 over 90 plus 21 over 90 equals space 27 over 90 space equals 3 over 10
Required probability = straight P left parenthesis straight R subscript 1 divided by straight R subscript 2 right parenthesis space equals space fraction numerator straight P left parenthesis straight R subscript 1 intersection straight R subscript 2 right parenthesis over denominator straight P left parenthesis straight R subscript 2 right parenthesis end fraction space equals space fraction numerator begin display style 1 over 15 end style over denominator begin display style 3 over 10 end style end fraction space equals 1 over 15 cross times 10 over 3 space equals 2 over 9.
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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).

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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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