CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A letter is taken out at random from 'ASSISTANT' and another is taken out from 'STATISTICS'. The probability that they are the same letters is


A
145
loader
B
1290
loader
C
1990
loader
D
None of these
loader

Solution

The correct option is C $$\cfrac{19}{90}$$
In 'ASSISTANT' and 'STATISTICS', the same letters are A,I,S,T

Probability of choosing $$\quad A=\cfrac { { _{  }^{ 2 }{ C } }_{ 1 } }{ { _{  }^{ 9 }{ C } }_{ 1 } } \times \cfrac { { _{  }^{ 1 }{ C } }_{ 1 } }{ { _{  }^{ 10 }{ C } }_{ 1 } } =\cfrac { 1 }{ 45 } $$

$$I=\cfrac { { _{  }^{ 1 }{ C } }_{ 1 } }{ { _{  }^{ 9 }{ C } }_{ 1 } } \times \cfrac { { _{  }^{ 2 }{ C } }_{ 1 } }{ { _{  }^{ 10 }{ C } }_{ 1 } } =\cfrac { 1 }{ 45 } $$

$$S=\cfrac { { _{  }^{ 3 }{ C } }_{ 1 } }{ { _{  }^{ 9 }{ C } }_{ 1 } } \times \cfrac { { _{  }^{ 3 }{ C } }_{ 1 } }{ { _{  }^{ 10 }{ C } }_{ 1 } } =\cfrac { 1 }{ 10 } $$

$$T=\cfrac { { _{  }^{ 2 }{ C } }_{ 1 } }{ { _{  }^{ 9 }{ C } }_{ 1 } } \times \cfrac { { _{  }^{ 3 }{ C } }_{ 1 } }{ { _{  }^{ 10 }{ C } }_{ 1 } } =\cfrac { 1 }{ 15 } $$

So, total probability
$$=\cfrac { 1 }{ 45 } +\cfrac { 1 }{ 45 } +\cfrac { 1 }{ 10 } +\cfrac { 1 }{ 15 } =\cfrac { 19 }{ 90 } $$

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image