A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting
·an eight given the card is a not a face card.
·a club given the card is red.
·a King, given that the card is red.
still very confused with this questions....
(a) 4/40 = 0.10
(b) 0 (A red card cannot be a club)
(c) 2/26 = 1/13
(because there are only two red kings and 26 red cards)
To solve these probability questions, we need to understand the concept of probability and how it relates to the given conditions.
First, let's determine the total number of cards in a standard deck, which is 52.
1. Probability of selecting an eight given that the card is not a face card:
A standard deck has 52 cards, and there are four eights in the deck. However, since we are considering cards that are not face cards, we need to exclude the 12 face cards, which include three eights. So, the number of eights that are not face cards is 4 - 3 = 1. Therefore, the probability of selecting an eight given that the card is not a face card is 1 / (52 - 12) = 1 / 40.
2. Probability of selecting a club given that the card is red:
A standard deck has 52 cards, and there are 13 clubs in the deck. However, since we are considering red cards, we need to exclude the black clubs. There are six black clubs, so the number of red clubs is 13 - 6 = 7. Therefore, the probability of selecting a club given that the card is red is 7 / 26.
3. Probability of selecting a King given that the card is red:
A standard deck has 52 cards, and there are four Kings in the deck. However, since we are considering red cards, we need to exclude the two black Kings. So, the number of red Kings is 4 - 2 = 2. Therefore, the probability of selecting a King given that the card is red is 2 / 26.
It's important to note that simplifications were made in each of these calculations. For instance, to find the probability of selecting an eight given that the card is not a face card, we assumed that all cards that are not face cards are equally likely to be selected. Similarly, we assumed that the deck has not been modified in any way (e.g., no cards are missing or extra). These assumptions may not always hold true in a real-world scenario, but they are often used in probability calculations for standard decks of playing cards.