Question

How would I solve the following questions from this: What is the probability of
a) drawing three aces in a row from a standard deck of cards when the drawn card is returned to the deck.
b) drawing three aces in a row from a standard deck of cards with no card replacement.
c) rolling 4 fair dice and getting an odd number on all 4 dice
d) being dealt five black cards off the top of a regular deck of well-shuffled cards.

Answer 1

a) As the card drawn is returned in the deck, the probability of getting an ace always remain the same which is equal to 1/13 which is because there is an ace in every 13th card.

Therefore the required probability here is computed as:

= (1/13)³

= 0.000455

Therefore 0.000455 is the required probability here.

b) As there is no replacement of card allowed here, the probability of getting three aces without replacement is computed here as:

Therefore 0.000181 is the required probability here.

c) There is a 0.5 probability of getting an odd number on any dice throw. Therefore the probability of getting an odd number on all 4 dice throws is computed as:

= 0.5*0.5*0.5*0.5

= 0.5⁴

= 0.0625

Therefore 0.0625 is the required probability here.

d) The probability of getting 5 black cards here is computed as:

Therefore 0.0253 is the required probability here.