A standard deck of cards has 52 cards in it. The cards are divided into 4 suits or 13 cards each.If one draws two cards at random from the deck of cards what is the probability that they are of the same suit ?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
13/52 * (13-1)/52-1) = ?
To calculate the probability that two cards drawn at random from a standard deck of cards are of the same suit, you first need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
When drawing two cards from a standard deck, the first card can be any of the 52 cards. After the first card is drawn, there are 51 cards remaining in the deck for the second draw. Therefore, the total number of possible outcomes is calculated as 52 * 51 = 2,652.
Number of favorable outcomes:
To calculate the number of favorable outcomes, you need to consider each of the four suits separately. For the first card drawn, you can pick any card from the deck (52 options). For the second card drawn, you need to choose a card from the same suit as the first card, which leaves you with only 12 options (since you already drew one card of that suit). Therefore, the number of favorable outcomes for each suit is 52 * 12 = 624.
Total number of favorable outcomes:
Since there are four suits, you need to multiply the number of favorable outcomes for each suit (624) by 4, resulting in a total of 2,496 favorable outcomes.
Now you can calculate the probability of drawing two cards of the same suit:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 2,496 / 2,652 = 0.941 = 94.1%
So, the probability of drawing two cards of the same suit from a standard deck is approximately 0.941, or 94.1%.