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A game consists of spinning arrow which comes to rest pointing at one of the numbers \[\mathbf{1},\text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{4},\text{ }\mathbf{5},\text{ }\mathbf{6},\text{ }\mathbf{7},\text{ }\mathbf{8},\text{ }\mathbf{9},\text{ }\mathbf{10},\text{ }\mathbf{11},\text{ }\mathbf{12};\] as shown below. If the outcomes are equally likely, find the probability that the pointer will point at: \[\left( \mathbf{i} \right)\text{ }\mathbf{6}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\] \[\left( \mathbf{ii} \right)\] an even number
A game consists of spinning arrow which comes to rest pointing at one of the numbers \[\mathbf{1},\text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{4},\text{ }\mathbf{5},\text{ }\mathbf{6},\text{ }\mathbf{7},\text{ }\mathbf{8},\text{ }\mathbf{9},\text{ }\mathbf{10},\text{ }\mathbf{11},\text{ }\mathbf{12};\] as shown below. If the outcomes are equally likely, find the probability that the pointer will point at: \[\left( \mathbf{i} \right)\text{ }\mathbf{6}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\] \[\left( \mathbf{ii} \right)\] an even number
CBSE | Class 10 | Exercise 13.3 | Selina | Statistics and Probability
A game consists of spinning arrow which comes to rest pointing at one of the numbers \[\mathbf{1},\text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{4},\text{ }\mathbf{5},\text{ }\mathbf{6},\text{ }\mathbf{7},\text{ }\mathbf{8},\text{ }\mathbf{9},\text{ }\mathbf{10},\text{ }\mathbf{11},\text{ }\mathbf{12};\] as shown below. If the outcomes are equally likely, find the probability that the pointer will point at: \[\left( \mathbf{i} \right)\text{ }\mathbf{6}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\] \[\left( \mathbf{ii} \right)\] an even number

Solution:

We have,

Total number of possible outcomes \[=\text{ }12\]

\[\left( i \right)\] Number of favorable outcomes for \[6\text{ }=\text{ }1\]6

Hence, \[P\left( the\text{ }pointer\text{ }will\text{ }point\text{ }at\text{ }6 \right)\text{ }=~1/12\]

\[\left( ii \right)\]Favorable outcomes for an even number are \[2,\text{ }4,\text{ }6,\text{ }8,\text{ }10,\text{ }12\]

So, number of favorable outcomes \[=\text{ }6\]

Hence, P(the pointer will be at an even number) \[=\text{ }6/12\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\]

 

i

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