10th Class Mathematics Solved Paper - Mathematics-2016 Outside Delhi Set-I

  • question_answer Three different coins are tossed together. Find the probability of getting (i) exactly two heads, (ii) at least two heads (iii) at least two tails.

    Answer:

    Set of possible outcomes
    \[=\{HHH,HHT,HTH,THH,HTT,THT,TTH,TTT\}\].
    (i) Let \[{{E}_{1}}\] be the event of getting exactly two heads
    \[\therefore \] Favourable outcomes \[=\{HHT,HTH,THH\}\]
    No. of favourable outcomes \[=3\]
                                        \[P({{E}_{2}})=\frac{3}{8}\]
     (ii) Let \[{{E}_{2}}\] be the event of getting at least two heads.
    \[\therefore \] Favourable outcomes \[=\{HHT,HTO,THH,HHH\}\]
    No. of favourable outcomes \[=4\]
                                        \[P({{E}_{2}})=\frac{4}{8}=\frac{1}{2}\]
     (iii) Let \[{{E}_{3}}\] be the event of getting at least two tails.
    \[\therefore \] Favourable outcomes \[=\{HTT,THT,TTH,TTT\}\]
                                        \[P({{E}_{3}})=\frac{4}{8}=\frac{1}{2}\]


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