Answer: The correct option is (c) [tex]\dfrac{1}{64}.[/tex]
Step-by-step explanation: We are given to find the probability of drawing a spade each time a card is drawn from a deck of 52 cards 3 times if replacement occurs each time.
Let S denote the sample space for the experiment of drawing a card from a deck of 52 cards
and A denote the event of drawing a spade from the deck of 52 cards.
Then, n(S) = 52 and n(A) = 13.
So, probability of event A will be
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{13}{52}=\dfrac{1}{4}.[/tex]
Since replacement occur each time, so the probability of drawing a spade each time a card is drawn from a deck of 52 cards 3 times will be
[tex]P=P(A)\times P(A)\times P(A)=\dfrac{1}{4}\times\dfrac{1}{4}\times\dfrac{1}{4}=\dfrac{1}{64}.[/tex]
Thus, the required probability is [tex]\dfrac{1}{64}.[/tex]
Option (c) is CORRECT.
