Two cards are drawn successively from a deck of 52 cards. Find the probability that the second card is higher in rank than the first card. Hint: Show that 1 = P(higher) + P(lower) + P(same) and use the fact that P(higher) = P(lower).
# Total number of cards in the deck
total_cards <- 52
# Probability of drawing a higher card on the second draw
probability_higher <- 1/2
# Probability of drawing a lower card on the second draw
probability_lower <- probability_higher
# Probability of drawing the same card on the second draw
probability_same <- 1/total_cards
# Total probability (sum of probabilities of all possible outcomes)
total_probability <- probability_higher + probability_lower + probability_same
# Probability that the second card drawn is higher in rank than the first card
probability_second_higher <- probability_higher / total_probability
probability_second_higher## [1] 0.490566