One card is drawn at random from a pack of well-shuffled deck of

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 Multiple Choice QuestionsShort Answer Type

811. A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.
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812.

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event 'the number is even', and B be the event, 'the number is red'. Are A and B independent?

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813. In the two dice experiment, if E is the even of getting the sum of numbers on dice as 11 and F is the event of getting a number other than 5 on the first die. find P (E and F). Are E and F independent events?

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814.

One card is drawn at random from a pack of well-shuffled deck of 52 cards. In which of the following cases are the events E and F are independent?
E : “the card drawn is a spade”
F : “the card drawn is an ace”.

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815.

One card is drawn at random from a pack of well-shuffled deck of 52 cards. In which of the following cases are the events E and F are independent?
E : “the card drawn is black”,
F : “the card drawn is a king”.


straight P left parenthesis straight E right parenthesis space equals space straight P space left parenthesis card space drawn space is space black right parenthesis space equals space 26 over 52 space equals space 1 half
straight P left parenthesis straight F right parenthesis space equals space straight P left parenthesis card space drawn space is space straight a space king right parenthesis space equals 4 over 52 space equals space 1 over 13

straight P left parenthesis straight E intersection straight F right parenthesis space equals space straight P left parenthesis card space drawn space is space black space and space card space drawn space is space king right parenthesis
space space space space space space space space space space space space space space space space equals space straight P left parenthesis card space drawn space is space straight a space black space king right parenthesis space equals space 2 over 52 space equals 1 over 26
Now, P(E) x P(F) = 1 half cross times 1 over 13 equals space 1 over 26

therefore space space space straight P left parenthesis straight E intersection straight F right parenthesis space equals space straight P left parenthesis straight E right parenthesis space cross times space straight P left parenthesis straight F right parenthesis
therefore space space space events space straight E space and space straight F space are space independent. space
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816.

One card is drawn at random from a pack of well-shuffled deck of 52 cards. In which of the following cases are the events E and F are independent?
E : “the card drawn is a king or queen”
F : “the card drawn is a queen or jack”.

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817.

A coin is tossed thrice. In which of the following cases are the events E and F independent?
E : the first throw results in head”.
F : “the last throw results in tail”.

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818.

A coin is tossed thrice. In which of the following cases are the events E and F independent?
E : “the number of heads is two”.
F : “the last throw results in head”.

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819.

A coin is tossed thrice. In which of the following cases are the events E and F independent?
E : “the number of heads is odd”.   
F : “the number of tails is odd”.

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 Multiple Choice QuestionsLong Answer Type

820. Three coins are tossed simultaneously. Consider the event E ‘three heads or three tails’, F ‘at least two heads' and G ‘at most two heads’. Of the pairs (E, F), (E, G) and (F, G), which are independent? Which are dependent?
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