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15/01/2022 4:05 pm
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Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is
(1) \(\frac{1}{8}\)
(2) \(\frac{5}{8}\)
(3) \(\frac{5}{16}\)
(4) 1
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15/01/2022 4:11 pm
Correct answer: (3) \(\frac{5}{16}\)
Explanation:
C - I '0' Head
TTT \(\Big(\frac{1}{2}\Big)^2\) \(\Big(\frac{1}{2}\Big)^3\) = \(\frac{1}{64}\)
C - II '1' Head
HTT \(\Big(\frac{3}{8}\Big)\)\(\Big(\frac{3}{8}\Big)\) = \(\frac{9}{64}\)
C - III '2' Head
HHT \(\Big(\frac{3}{8}\Big)\)\(\Big(\frac{3}{8}\Big)\) = \(\frac{9}{64}\)
C - IV '3' Head
HHH \(\Big(\frac{1}{8}\Big)\)\(\Big(\frac{1}{8}\Big)\) = \(\frac{1}{64}\)
Total probability = \(\Big(\frac{5}{16}\Big)\)