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Probability

Short 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).

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760.
A coin is tossed three times, where
E : head on third toss, F : heads on first two tosses

Here S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
E : head on third toss
$therefore$ E = {HHH, HTH, THH, TTH}
and F : heads on first two tosses
$therefore space space space straight F space equals space left curly bracket HHH comma space HHT right curly bracket therefore space space straight E intersection straight F space equals space left curly bracket HHH right curly bracket therefore space space straight P left parenthesis straight E right parenthesis space equals space 4 over 8 space equals space 1 half comma space space space straight P left parenthesis straight F right parenthesis space equals space 2 over 8 space equals space 1 fourth comma space space space straight P left parenthesis straight E intersection straight F right parenthesis space equals space 1 over 8$
$straight P left parenthesis straight E space left enclose straight F right parenthesis space equals space fraction numerator straight P left parenthesis straight E intersection straight F right parenthesis over denominator straight P left parenthesis straight F right parenthesis end fraction space equals fraction numerator begin display style 1 over 8 end style over denominator begin display style 2 over 8 end style end fraction space equals space 1 half$