FAQs on Probability Card experiment Problem Solving 1 Video Lecture  Probability For Beginners  Mathematics and Statistics  Class 10
1. What is the probability of drawing a heart from a standard deck of cards? 

Ans. In a standard deck of cards, there are 52 cards in total, and 13 of them are hearts. Therefore, the probability of drawing a heart from a standard deck of cards is 13/52, which simplifies to 1/4.
2. If two cards are drawn from a standard deck without replacement, what is the probability that both cards are red? 

Ans. In a standard deck of cards, there are 26 red cards out of 52. When the first card is drawn, there are 26 red cards out of 52 remaining in the deck. So, the probability of drawing a red card on the first draw is 26/52, which simplifies to 1/2. After the first card is drawn, there are 25 red cards out of 51 remaining in the deck. Therefore, the probability of drawing a red card on the second draw, given that the first card was red, is 25/51. To find the probability of both events occurring, we multiply the probabilities together: (1/2) * (25/51) = 25/102.
3. What is the probability of drawing a face card (jack, queen, or king) from a standard deck of cards? 

Ans. In a standard deck of cards, there are 12 face cards (4 jacks, 4 queens, and 4 kings) out of 52. Therefore, the probability of drawing a face card from a standard deck of cards is 12/52, which simplifies to 3/13.
4. If three cards are drawn from a standard deck without replacement, what is the probability that at least one of them is a spade? 

Ans. In a standard deck of cards, there are 13 spades out of 52. When the first card is drawn, there are 13 spades out of 52 remaining in the deck. So, the probability of drawing a spade on the first draw is 13/52, which simplifies to 1/4. After the first card is drawn, there are 12 spades out of 51 remaining in the deck. Therefore, the probability of not drawing a spade on the second draw, given that the first card was not a spade, is 39/51. Similarly, for the third draw, the probability of not drawing a spade, given that the first two cards were not spades, is 38/50. To find the probability of at least one spade, we subtract the probability of no spades from 1: 1  (39/51 * 38/50) = 1219/1875.
5. If four cards are drawn from a standard deck without replacement, what is the probability that they are all of the same suit? 

Ans. In a standard deck of cards, there are 13 cards of each suit (hearts, diamonds, clubs, and spades). When the first card is drawn, there are 13 cards of the same suit out of 52 remaining in the deck. So, the probability of drawing a card of the same suit as the first card is 13/52, which simplifies to 1/4. After the first card is drawn, there are 12 cards of the same suit out of 51 remaining in the deck. Similarly, for the third and fourth draws, the probability of drawing a card of the same suit as the previous ones is 11/50 and 10/49, respectively. To find the probability of all four cards being of the same suit, we multiply the probabilities together: (1/4) * (12/51) * (11/50) * (10/49) = 110/4165.