Final answer:
The probabilities of selecting a five or a six, a five, six, or three, and a two or any club from a standard deck of 52 cards are 2/13, 3/13, and 4/13 respectively, after accounting for the total number of cards and any overlap between the categories.
Step-by-step explanation:
To calculate the probability of drawing a certain card from a standard deck of 52 cards, we look at the number of favorable outcomes over the number of total possible outcomes.
A) Probability of Selecting a Six or a Five
There are 4 sixes and 4 fives in the deck, making a total of 8 cards that are either a six or a five. Thus, the probability is:
P(six or five) = Number of Sixes and Fives / Total Number of Cards = 8/52 = 2/13
B) Probability of Selecting a Six, Five, or Three
Adding the fours threes to the previous total, we have 4 threes, 4 fives, and 4 sixes, which adds up to 12 favorable cards. Therefore, the probability is:
P(six, five, or three) = Number of Threes, Fives, and Sixes / Total Number of Cards = 12/52 = 3/13
C) Probability of Selecting a Two or a Club
There are 4 twos in the deck and 13 clubs. However, one of the twos is also a club, so we have to account for this overlap by subtracting it once:
P(two or a club) = (Number of Twos + Number of Clubs - Overlap) / Total Number of Cards = (4 + 13 - 1) / 52 = 16/52 = 4/13