consider shuffling a standard 52 deck of cards and drawing one which is black. what is the probability that the card is a 4,5,or 6
To find the probability of drawing a 4, 5, or 6 from a standard 52-card deck after shuffling, we first need to determine the total number of favorable outcomes and the total number of possible outcomes.
1. Total Number of Favorable Outcomes:
- There are four 4s in a deck (4 of clubs, 4 of spades, 4 of hearts, and 4 of diamonds).
- There are four 5s in a deck (5 of clubs, 5 of spades, 5 of hearts, and 5 of diamonds).
- There are four 6s in a deck (6 of clubs, 6 of spades, 6 of hearts, and 6 of diamonds).
- So, the total number of favorable outcomes is 4 + 4 + 4 = 12.
2. Total Number of Possible Outcomes:
- In a shuffled deck, the total number of cards is 52.
- The favorable outcomes are the black cards, which include clubs and spades. There are 26 black cards in the deck.
- So, the total number of possible outcomes is 26.
Therefore, the probability of drawing a black card that is a 4, 5, or 6 is given by:
Probability = (Number of Favorable Outcomes) / (Number of Possible Outcomes)
= 12 / 26
= 6 / 13
Hence, the probability that the card drawn is a 4, 5, or 6, given that it is black, is 6/13.