Using a standard deck of 52 cards find each probability.
1.)King, queen, or black card
2.)Spade or hearts card
I will assume you are drawing one card
number of favourable outcomes
= 4 kings + 4 queens + 26 black cards - 2black kings - 2black queens
= 30
prob(king or queen or black card ) = 30/52 = 15/26
spade or hearts = 13 + 4 - 1 = 16
prob = 16/52 = 4/13
To find the probability of an event, we need to divide the number of favorable outcomes by the total number of possible outcomes. Let's calculate the probabilities for the given cases:
1.) King, queen, or black card:
- Favorable Outcomes: There are 4 kings and 4 queens in a standard deck, so a total of 8 favorable outcomes (4 kings + 4 queens). Additionally, there are 26 black cards (spades and clubs) in the deck.
- Total Outcomes: A standard deck has 52 cards.
- Probability: P(King, queen, or black card) = (8 + 26) / 52 = 34 / 52 = 17 / 26 ≈ 0.654 or 65.4%.
2.) Spade or hearts card:
- Favorable Outcomes: There are 13 spades and 13 hearts in a standard deck, so a total of 26 favorable outcomes (13 spades + 13 hearts).
- Total Outcomes: A standard deck has 52 cards.
- Probability: P(Spade or hearts card) = 26 / 52 = 1 / 2 = 0.5 or 50%.
Therefore, the probabilities are:
1.) P(King, queen, or black card) ≈ 0.654 or 65.4%
2.) P(Spade or hearts card) = 0.5 or 50%.