TIFR CSE 2013 | Part A | Question: 14

Question

An unbiased die is thrown $n$ times. The probability that the product of numbers would be even is

• A. $\dfrac{1}{(2n)}$
• B. $\dfrac{1}{[(6n)!]}$
• C. $1 - 6^{-n}$
• D. $6^{-n}$
• E. None of the above

Answer 1

Odd # = odd x odd

In all the other cases it is even.

	n=1	n=2	n=3	n=n
# of odds	3	$3^{2}$	$3^{3}$	$3^{n}$
# of evens	6 - 3	$6^{2}$ - $3^{2}$	$6^{3} - 3^{3}$	$6^{n} - 3^{n}$

Probability = $\frac{6^{n}-3^{n}}{6^{n}}$ = $1-(\frac{1}{2})^{n}$