JEE Main & Advanced Mathematics Probability Question Bank

done Definition of various terms Total Questions - 7

• question_answer1)
  Two coins are tossed. Let A be the event that the first coin shows head and B be the event that the second coin shows a tail. Two events A and B are [MP PET 1989]
  A)
                  Mutually exclusive done clear
  B)
                  Dependent done clear
  C)
                  Independent and mutually exclusive done clear
  D)
                  They are basically independent. done clear
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• question_answer2)
  If  \[P\,({{A}_{1}}\cup {{A}_{2}})=1-P(A_{1}^{c})\,P(A_{2}^{c})\] where c stands for complement, then the events \[{{A}_{1}}\] and \[{{A}_{2}}\] are [MP PET 1989]
  A)
                  Mutually exclusive done clear
  B)
                  Independent done clear
  C)
                  Equally likely         done clear
  D)
                  None of these done clear
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• question_answer3)
  Two fair dice are tossed. Let A be the event that the first die shows an even number and B be the event that the second die shows an odd number. The two event A and B are [IIT 1979]
  A)
                  Mutually exclusive done clear
  B)
                  Independent and mutually exclusive done clear
  C)
                  Dependent done clear
  D)
                  None of these done clear
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• question_answer4)
  A card is drawn from a pack of 52 cards. If A = card is of diamond, B = card is an ace and \[A\cap B=\]card is ace of diamond, then events A and B are
  A)
                  Independent          done clear
  B)
                  Mutually exclusive done clear
  C)
                  Dependent             done clear
  D)
                  Equally likely done clear
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• question_answer5)
  If A and B are two independent events, then A and \[\bar{B}\] are
  A)
                  Not independent   done clear
  B)
                  Also independent done clear
  C)
                  Mutually exclusive done clear
  D)
                  None of these done clear
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• question_answer6)
  Let A, B, C be three mutually independent events. Consider the two statements \[{{S}_{1}}\]and \[{{S}_{2}}\]                 \[{{S}_{1}}\,\,:\,\,A\] and \[B\cup C\] are independent                 \[{{S}_{2}}\,\,:\,\,A\] and \[B\cap C\] are independent                 Then [IIT 1994]
  A)
                  Both \[{{S}_{1}}\] and \[{{S}_{2}}\] are true done clear
  B)
                  Only \[{{S}_{1}}\] is true done clear
  C)
                  Only \[{{S}_{2}}\] is true done clear
  D)
                  Neither \[{{S}_{1}}\] nor \[{{S}_{2}}\] is true done clear
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• question_answer7)
  If \[P(A)=2/3\], \[P(B)=1/2\] and \[\text{ }P(A\cup B)=5/6\] then events A and B are                                 [Kerala (Engg.)  2002]
  A)
                  Mutually exclusive done clear
  B)
                  Independent as well as mutually exhaustive done clear
  C)
                  Independent          done clear
  D)
                  Dependent only on A done clear
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