Explanation:
To find the probability of selecting 5 cards that are all from the same suit in a deck of 52 cards, we can use combinatorics and the concept of dependent events.
a) All 5 Cards Are Spades
The probability of drawing the first spade is 13/52. Since the cards are not replaced after being drawn, the probability of drawing subsequent spades changes. The probability for all five cards being spades is calculated by multiplying the probabilities for each draw:
P(5 spades in a row) = (13/52) *(12/51) *(11/50) *(10/49)*(9/48)
b) All Five Cards Are the Same Suit
Since there are four suits and the question doesn't specify which suit to draw from, we must calculate the probability for one suit and then multiply it by four (the number of suits):
P(5 cards of the same suit) = 4 *P(5 spades in a row) = 4*(13*12*11*10*9)/(13^5)
c) 4 Aces and 1 King
The probability of drawing four aces and one king without replacement is:
P(4 Aces and 1 King) = (4/52)*(3/51) *(2/50)*(1/49)*(4/48)
