Question
Mohit is a teacher and he teach some students in two
(Morning & evening) slots. There are 5 boys and ‘x’ girls in morning slot, while there are ‘x’ boys and 8 girls in evening slot. If one student is chosen at random from any slot, then the probability of being girl is 5/9. Which of the following can be the value of ‘x’? I. 10 II. 4 III. 3 IV. 5 V. 6Solution
Probability for being girl from morning slot = (1/2) × (x/(x+5)) Probability for being girl from evening slot = (1/2) × (8/(x+8)) ATQ – 1/2 [x/(x+5)+(8/(x+8))]=5/9 10/9=(x(x+8)+8(x+5))/(x+8)(x+5)  10/9=(x2+8x+8x+40)/(x2+13x+40) 10x2+130x+400=9x2+144x+360 x2–14x+40=0 x2–10x–4x+40=0  x(x –10) –4(x –10)=0  x=10,4  So, both I and II follow
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