NIELIT 2017 July Scientist B (IT) - Section B: 23

Question

The probability that top and bottom cards of a randomly shuffled deck are both aces is:

• A. $4/52\times 4/52$
• B. $4/52\times 3/52$
• C. $4/52\times 3/51$
• D. $4/52\times 4/51$

Answer 1

Option C

There are 4 aces in a deck

Probability of 1^st card drawn to be ace = $\frac{\binom{4}{1}}{\binom{52}{1}} = \frac{4}{52}$

Now, Remaining aces $= 4 – 1 = 3$ and Remaining cards $= 52 – 1 = 51$

So, Probability of 2^nd card drawn to be ace = $\frac{\binom{3}{1}}{\binom{51}{1}} = \frac{3}{51}$

Hence, Total Probability that top and bottom cards of a randomly shuffled deck are both aces is $=\mathbf{\frac{4}{52}\times \frac{3}{51}}$