Can someone please check my answers?
A card is randomly drawn from a standard deck of 52 cards. Find the probability of drawing the indicated card.
1.Not an ace. =12/13
2.A face card and a four. =4/13
3.A heart or a diamond. =1/2
4.A six or a seven. = 2/13
5.An ace and a spade. =4/13
6. You and your best friend are members of a high school tennis team. The coach is about to pick one player to be captain of the team. You estimate that there is a 34% chance you will be picked and a 54% chance that your best friend will be picked. What is the probability that either you or your best friend will be picked? =88%
Let's evaluate your answers step-by-step:
1. Not an ace.
In a standard deck of 52 cards, there are 4 aces. Therefore, the probability of drawing a card that is not an ace is: (52 - 4) / 52 = 48 / 52 = 12/13.
Your answer is correct.
2. A face card and a four.
There are 12 face cards in a deck (4 jacks, 4 queens, 4 kings) and 2 fours. However, one of the fours is also a face card. So, we have 11 cards that satisfy the condition out of 52 total cards. The probability of drawing a face card and a four is: 11 / 52 = 11/52.
Your answer is incorrect. The correct probability is 11/52.
3. A heart or a diamond.
In a standard deck of 52 cards, there are 13 hearts and 13 diamonds. Therefore, the total probability of drawing either a heart or a diamond is: 13 / 52 + 13 / 52 = 26 / 52 = 1/2.
Your answer is correct.
4. A six or a seven.
There are four sixes and four sevens in a standard deck of 52 cards. Therefore, the probability of drawing either a six or a seven is: 8 / 52 = 2 / 13.
Your answer is correct.
5. An ace and a spade.
There are four aces and 13 spades in a standard deck of 52 cards. Therefore, the probability of drawing an ace and a spade is: 4 / 52 = 1 / 13.
Your answer is correct.
6. Probability of either you or your best friend being picked as captain.
To find the probability of either you or your best friend being picked, you need to add the individual probabilities of each event happening:
P(you) = 34% = 0.34
P(best friend) = 54% = 0.54
P(you or best friend) = P(you) + P(best friend) = 0.34 + 0.54 = 0.88.
Your answer is correct. The probability that either you or your best friend will be picked as captain is 88%.
To check the answers, we can use a simple method: divide the number of desired outcomes by the total number of possible outcomes.
1. Not an ace: There are 52 cards in total, and 4 of them are aces. So, there are 52-4=48 cards that are not an ace. The probability of drawing a card that is not an ace is 48/52, which simplifies to 12/13.
2. A face card and a four: There are 12 face cards (3 suits, each with 4 face cards) and 4 fours in the deck. The probability of drawing a face card and a four is (12 * 4) / 52 = 48 / 52, which simplifies to 4/13.
3. A heart or a diamond: There are 13 hearts and 13 diamonds in the deck, so a total of 26 cards that are either a heart or a diamond. The probability of drawing a heart or a diamond is 26 / 52, which simplifies to 1/2.
4. A six or a seven: There are 4 sixes and 4 sevens in the deck. So, the probability of drawing a six or a seven is (4 + 4) / 52 = 8 / 52, which simplifies to 2/13.
5. An ace and a spade: There are 4 aces in the deck, and 13 spades. The probability of drawing an ace and a spade is (4 * 13) / 52 = 52 / 52, which simplifies to 1.
6. For the probability that either you or your best friend will be picked as captain, you need to add the individual probabilities of being picked. So, the probability is 34% + 54%, which equals 88%. However, it's important to note that these probabilities assume that only one person will be chosen, and there are no other factors affecting the decision.