Statistics And Probability Question 234
Question: A bag has 13 red, 14 green and 15 black balls. The probability of getting exactly 2 blacks on pulling out 4 balls is $ P_1. $ Now the number of each colour ball is doubled and 8 balls are pulled out. The probability of getting exactly 4 blacks is $ P_2. $ Then
Options:
A) $ P_1=P_2 $
B) $ P_1>P_2 $
C) $ P_1<P_2 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
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$ P_1=\frac{{}^{15}C_2\times {}^{27}C_2}{{}^{42}C_4}=\frac{27}{82} $ and $ P_2=\frac{{}^{30}C_4\times {}^{54}C_4}{{}^{84}C_8}=\frac{17\,.\,29\,.\,45\,.\,53}{11\,.\,79\,.\,82\,.\,83} $ (After simplification) Hence $ P_1>P_2. $
BETA
