Verified Solution • 2025–26 Session moderate

QJEEM21Ma0379: JEE Main 2021 Mathematics - Class 12 JEEM21Ma0379 Solution: A pack of cards has one card missing. Two cards are drawn…

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is :

Multiple Choice Options

  • A 3950{{39} \over {50}}
  • B 34{{3} \over {4}}
  • C 22425{{22} \over {425}}
  • D 52867{{52} \over {867}}

Step-by-Step Verified Solution

Consider the events,

E1 = missing card is spade

E2 = missing card is not a spade

A = Two spade cards are drawn

P(E1)=14P\left( {{E_1}} \right) = {1 \over 4}
P(E2)=34P\left( {{E_2}} \right) = {3 \over 4}

P(AE1)=12C251C2P\left( {{A \over {{E_1}}}} \right) = {{{}^{12}{C_2}} \over {{}^{51}{C_2}}}

P(AE2)=13C251C2P\left( {{A \over {{E_2}}}} \right) = {{{}^{13}{C_2}} \over {{}^{51}{C_2}}}

P(E2A)=P(AE2).P(E2)P(AE1).P(E1)+P(AE2).P(E2)P\left( {{{{E_2}} \over A}} \right) = {{P\left( {{A \over {{E_2}}}} \right).P\left( {{E_2}} \right)} \over {P\left( {{A \over {{E_1}}}} \right).P\left( {{E_1}} \right) + P\left( {{A \over {{E_2}}}} \right).P\left( {{E_2}} \right)}}

=13C251C2.3412C251C2.14+13C251C2.34= {{{{{}^{13}{C_2}} \over {{}^{51}{C_2}}}.{3 \over 4}} \over {{{{}^{12}{C_2}} \over {{}^{51}{C_2}}}.{1 \over 4} + {{{}^{13}{C_2}} \over {{}^{51}{C_2}}}.{3 \over 4}}}

= 3950{{39} \over {50}}

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