Suppose that you randomly draw one card from a standard deck of 52 cards. After writing down which card was drawn, you place the card back in the deck, shuffle the deck, and draw another card. You repeat this process until you have drawn 12 cards in all. What is the probability of drawing at least 6 diamonds?

Solution

S u pp ose t ha t yo u r an d o m l y d r a w o n e c a r d f ro m a s t an d a r d d ec k o f 52 c a r d s . A f t er w r i t in g d o w n w hi c h c a r d w a s d r a w n, yo u pl a ce t h e c a r d ba c k in t h e d ec k, s h u ff l e t h e d ec k, an d d r a w an o t h er c a r d . Y o u re p e a t t hi s p rocess u n t i l yo u ha v e d r a w n 12 c a r d s in a ll . Wha t i s t h e p ro babi l i t y o f d r a w in g a t l e a s t 6 d iam o n d s ?

0

Solution steps

The probability of drawing at least 6 diamonds is 0 since this never occurs.

= 0