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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: \[\left( \mathbf{v} \right)\]a number less than or equal to \[\mathbf{9}\] \[\left( \mathbf{vi} \right)\] a number between \[\mathbf{3}\]and \[\mathbf{11}\]
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: \[\left( \mathbf{v} \right)\]a number less than or equal to \[\mathbf{9}\] \[\left( \mathbf{vi} \right)\] a number between \[\mathbf{3}\]and \[\mathbf{11}\]
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: \[\left( \mathbf{v} \right)\]a number less than or equal to \[\mathbf{9}\] \[\left( \mathbf{vi} \right)\] a number between \[\mathbf{3}\]and \[\mathbf{11}\]

Solution:

\[\left( v \right)\] Favorable outcomes for a number less than or equal to \[9\text{ }are\text{ }1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6,\text{ }7,\text{ }8,\text{ }9\]

So, number of favorable outcomes \[=\text{ }9\]

Hence\[,\text{ }P\left( the\text{ }pointer\text{ }will\text{ }be\text{ }at\text{ }a\text{ }number\text{ }less\text{ }than\text{ }or\text{ }equal\text{ }to\text{ }9 \right)\text{ }=\text{ }9/12\text{ }=\text{ }3/4\]

\[\left( vi \right)\] Favorable outcomes for a number between \[3\text{ }and\text{ }11\text{ }are\text{ }4,\text{ }5,\text{ }6,\text{ }7,\text{ }8,\text{ }9,\text{ }10\]

So. number of favorable outcomes \[=\text{ }7\]

Hence, P(the pointer will be at a number between \[3\text{ }and\text{ }11)\text{ }=~7/12\]

 

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