AP EAMCET · Maths · Probability
From out of 100 enrolled students, two sections of strength 40 and 60 are formed. If you and your friend are among those 100 students, then the probability that both of you are placed in the same section is
- A \(\frac{{ }^{98} \mathrm{C}_{40}+{ }^{98} \mathrm{C}_{58}}{{ }^{100} \mathrm{C}_{40}}\)
- B \(\frac{{ }^{40} \mathrm{C}_2+{ }^{60} \mathrm{C}_2}{{ }^{100} \mathrm{C}_2}\)
- C \(\frac{{ }^{98} \mathrm{C}_{60}+{ }^{98} \mathrm{C}_{38}}{{ }^{100} \mathrm{C}_{60}}\)
- D \(\frac{{ }^{98} \mathrm{C}_{58}+{ }^{98} \mathrm{C}_0}{{ }^{100} \mathrm{C}_2}\)
Answer & Solution
Correct Answer
(B) \(\frac{{ }^{40} \mathrm{C}_2+{ }^{60} \mathrm{C}_2}{{ }^{100} \mathrm{C}_2}\)
Step-by-step Solution
Detailed explanation
Total no. of ways of selecting 2 students out of 100 \(={ }^{100} C_2\) No. of ways in which both of us enter the same section \(={ }^{40} C_2+{ }^{60} C_2\) \(\therefore\) Required probability \(=\frac{{ }^{40} C_2+{ }^{60} C_2}{{ }^{100} C_2}\)
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