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10th Class Mathematics Probability Question Bank Probability

  • question_answer
    A coin is tossed twice if the coin shows head it is tossed again but if it shows a tail then a die is tossed. If 8 possible outcomes are equally likely, find the probability that the die shows a number greater than 4, if it is known that the first throw of the coin results in a tail.

    A)  \[\frac{1}{3}\]             

    B)  \[\frac{2}{3}\]

    C)  \[\frac{2}{5}\]                         

    D)  \[\frac{4}{15}\]

    Correct Answer: A

    Solution :

    (a): Here sample space is given as, \[S=\{HH,HT,T1,T2,T3,T4,T5,T6\}\]Let a be the event that the die shows a number greater than 4 and B be the event that the first throw of the coin results in a tail then, \[A=\{T5,T6\}\] \[B=\{T1,T2,T3,T4,T5,T6\}\] \[\therefore \] Required probability \[\Rightarrow \]   \[P\left( \frac{A}{B} \right)=\frac{P(A\cap B)}{P(B)}=\frac{\frac{2}{8}}{\frac{6}{8}}=\frac{1}{3}\]           


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