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Home » A game consists of spinning arrow which comes to rest pointing at one of the numbers     as shown below. If the outcomes are equally likely, find the probability that the pointer will point at:     a prime number     a number greater than    
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:

    \[~~~\left( \mathbf{iii} \right)\]

a prime number

    \[\left( \mathbf{iv} \right)\]

a number greater than

    \[\mathbf{8}\]

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:

    \[~~~\left( \mathbf{iii} \right)\]

a prime number

    \[\left( \mathbf{iv} \right)\]

a number greater than

    \[\mathbf{8}\]

Solution:

    \[\left( iii \right)\]

Favorable outcomes for a prime number are

    \[2,\text{ }3,\text{ }5,\text{ }7,\text{ }11\]

So, number of favorable outcomes

    \[~=\text{ }5\]

Hence, P(the pointer will be at a prime number)

    \[=~5/12\]

    \[\left( iv \right)\]

Favorable outcomes for a number greater than

    \[8\text{ }are\text{ }9,\text{ }10,\text{ }11,\text{ }12\]

So, number of favorable outcomes

    \[=\text{ }4\]

Hence,

    \[P\left( the\text{ }pointer\text{ }will\text{ }be\text{ }at\text{ }a\text{ }number\text{ }greater\text{ }than\text{ }8 \right)\text{ }=\text{ }4/12\text{ }=\text{ }1/3\]

i

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