Question

what is 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? a.1/2197 b.11/850 c.1/64 d.3/4

Answer 1

Answer: The correct option is (c)
`(1)/(64).`

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

`P(A)=(n(A))/(n(S))=(13)/(52)=(1)/(4).`

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

`P=P(A)* P(A)* P(A)=(1)/(4)*(1)/(4)*(1)/(4)=(1)/(64).`

Thus, the required probability is
`(1)/(64).`

Option (c) is CORRECT.