Hundred identical cards are numbered from The cards The cards are well shuffled and then a card is drawn. Find the probability that the number on card drawn is:

    \[\left( \mathbf{iii} \right)\]

between

    \[\mathbf{40}\]

and

    \[\mathbf{60}\]

    \[\left( \mathbf{iv} \right)\]

greater than

    \[\mathbf{85}\]

Hundred identical cards are numbered from The cards The cards are well shuffled and then a card is drawn. Find the probability that the number on card drawn is:

    \[\left( \mathbf{iii} \right)\]

between

    \[\mathbf{40}\]

and

    \[\mathbf{60}\]

    \[\left( \mathbf{iv} \right)\]

greater than

    \[\mathbf{85}\]

Solution:

    \[\left( iii \right)\]

From numbers

    \[1\text{ }to\text{ }100\]

, there are

    \[19\]

numbers which are between

    \[40\text{ }and\text{ }60\text{ }i.e.~\{41,\text{ }42\]

,

    \[43,\text{ }44,\text{ }45,\text{ }46,\text{ }47,\text{ }48,\text{ }49,\text{ }50,\text{ }51,\text{ }52,\text{ }53,\text{ }54,\text{ }55,\text{ }56,\text{ }57,\text{ }58,\text{ }59\}\]

So, favorable number of events

    \[=\text{ }n\left( E \right)\text{ }=\text{ }19\]

Hence, probability of selecting a card between

    \[40\text{ }and\text{ }60\text{ }=\text{ }n\left( E \right)/\text{ }n\left( S \right)\text{ }=\text{ }19/100\]

    \[\left( iv \right)\]

From numbers

    \[1\text{ }to\text{ }100\]

, there are

    \[15\]

numbers which are greater than 85 i.e. 

    \[\{86,\text{ }87,\text{ }\ldots .,\]

,

    \[98,\text{ }99,\text{ }100\}\]

So, favorable number of events

    \[=\text{ }n\left( E \right)\text{ }=\text{ }15\]

Hence, probability of selecting a card with a number greater than

    \[85\text{ }=\text{ }n\left( E \right)/\textn\left( S \right)\text{ }=\text{ }15/100\text{ }=\text{ }3/20\]