You and a friend each have a standard and well-shuffled 52-card deck of cards. You draw a card from your deck and your friend draws a card from her deck. Match the following results with their respective probabilities:
Question 1 answers
You each pick the 10 of spades. Read Answer Items
One of you picks the 10 of spades and the other picks the 10 of clubs. Read Answer Items
You pick the 10 of spades and your friend picks the 10 of clubs. Read Answer Items
Your friend picks a red face card and you pick the jack of hearts or the queen of spades. Read Answer Items
To find the probabilities of the given events, we need to calculate the total number of possible outcomes and the number of favorable outcomes for each event.
First, let's determine the total number of possible outcomes. When you draw a card from your deck, there are 52 possible cards you can choose from. Similarly, when your friend draws a card from her deck, there are also 52 possible cards she can choose from. Since these two events are independent, the total number of possible outcomes is the product of the individual card choices, which is 52 * 52 = 2,704.
Now, let's calculate the number of favorable outcomes for each event:
1. You each pick the 10 of spades: There is only 1 card of 10 of spades in each deck, so the number of favorable outcomes is 1 * 1 = 1.
2. One of you picks the 10 of spades and the other picks the 10 of clubs: Since there is only 1 card of 10 of spades and 1 card of 10 of clubs in each deck, there are two ways this can happen: you picking the 10 of spades and your friend picking the 10 of clubs, or vice versa. Therefore, the number of favorable outcomes is 2.
3. You pick the 10 of spades and your friend picks the 10 of clubs: As mentioned above, there is only 1 card of 10 of spades and 1 card of 10 of clubs in each deck, so this event can happen in only one way. Hence, the number of favorable outcomes is 1.
4. Your friend picks a red face card and you pick the jack of hearts or the queen of spades: In each deck, there are 2 red face cards (king and queen of hearts) and 2 black face cards (jack and queen of spades). Therefore, the number of favorable outcomes is 2 (red face card) * 2 (jack of hearts or queen of spades) = 4.
Now, let's match the probabilities with the respective events:
1. Probability of both picking the 10 of spades: 1 favorable outcome / 2,704 total outcomes.
2. Probability of one picking the 10 of spades and the other picking the 10 of clubs: 2 favorable outcomes / 2,704 total outcomes.
3. Probability of you picking the 10 of spades and your friend picking the 10 of clubs: 1 favorable outcome / 2,704 total outcomes.
4. Probability of your friend picking a red face card and you picking the jack of hearts or the queen of spades: 4 favorable outcomes / 2,704 total outcomes.
Now you have the probabilities for the given events, calculated by considering the total number of outcomes and the number of favorable outcomes for each event.