Sophie has randomly chosen a card from a standard deck and placed it in her pocket. She is going to randomly choose a second card from the deck. a.What is the probability that she chooses the same card as the one in her pocket
b. what is the probability that the second card has the same suit as the first card?
To solve this problem, we need to understand the concept of probability and how it applies to the given scenario.
a. The probability that Sophie chooses the same card as the one in her pocket:
A standard deck of cards contains 52 cards, and Sophie has already chosen one. Therefore, there are now 51 cards left in the deck. Since she has randomly chosen a card from the deck, any of the 51 remaining cards in the deck could be the second card she selects. However, only one of those 51 cards matches the one in her pocket. So, the probability of Sophie choosing the same card as the one in her pocket is 1 out of 51, which can be expressed as:
P(same card) = 1/51
b. The probability that the second card has the same suit as the first card:
A standard deck of cards contains four suits: diamonds, clubs, hearts, and spades. Each suit has 13 cards. Since Sophie has already chosen a card from the deck, there is now only one card of that suit left in the deck. Therefore, out of the remaining 51 cards, only 12 of them match the suit of the first card. The probability of Sophie choosing a card with the same suit as the first card can be expressed as:
P(same suit) = 12/51
In summary:
a. Probability of choosing the same card = 1/51
b. Probability of choosing the same suit = 12/51
a. The probability is zero. There is only one of each kind of card in a deck.
b. 12/51