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?
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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?


Let R1, R2 be the events that red ball is drawn in the first and second draw. Here balls are drawn with replacement.
therefore space space space space straight P left parenthesis straight R subscript 1 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 3 over 10 space equals 9 over 100.

straight P left parenthesis straight R subscript 2 right parenthesis space equals space straight P left parenthesis apostrophe straight R subscript 1 space straight R subscript 2 apostrophe space 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

            equals space 3 over 10 cross times 3 over 10 plus 7 over 10 cross times 3 over 10 equals space 9 over 100 plus 21 over 100 equals 30 over 100.
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 space intersection space straight R subscript 2 right parenthesis over denominator straight P left parenthesis straight R subscript 2 right parenthesis end fraction space equals fraction numerator begin display style 9 over 100 end style over denominator begin display style 30 over 100 end style end fraction space equals 3 over 10.
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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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