You draw 4 cards from a deck of 52 cards with replacement. What are the probabilities of drawing a black card on each of your four trials?
Solution:
As, in a pack of cards, there are 26 black cards and 26 red cards.
Probability of an event = \(\frac{\text{total favorable outcome}}{\text{total possible outcome}}\)
Probability of drawing a black card from a pack of 52 cards = \(\frac{26}{52}=\frac{1}{2}\)
As each card drawn is replaced,Each black card draw is an independent with another black card draw.
Probabilities of drawing a black card on each of four trial=
\(\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=[\frac{1}{2}]^4\)