You are randomly selecting one catches on a 52 card deck.find the probability of selecting:
a 2 or a 3
I got 2/13
A red 2 or a black 3
I got 1/13
I want to make sure it is correct
This is very urgent
Thanks
agree 8/52 = 2/13
agree 4/52 = 1/13
Thank you
To verify the probabilities you calculated, let's go through the steps to obtain the correct answers.
1. Probability of selecting a 2 or a 3:
In a standard deck of 52 cards, there are 4 suits (hearts, diamonds, clubs, and spades) and each suit contains one 2 and one 3. So, there are a total of 8 (4 twos and 4 threes) cards that are either a 2 or a 3.
To calculate the probability, we need to divide the number of favorable outcomes (selecting a 2 or a 3) by the total number of possible outcomes (selecting any card from the deck).
Total possible outcomes = 52 (as there are 52 cards in a deck)
Favorable outcomes = 8 (as determined earlier)
Therefore, the probability of selecting a 2 or a 3 is 8/52, which simplifies to 2/13.
So, your calculation for the probability of selecting a 2 or a 3 is correct.
2. Probability of selecting a red 2 or a black 3:
To calculate this probability, we need to determine the number of favorable outcomes and the total possible outcomes.
For a red 2, there is only one card that satisfies this condition: the 2 of hearts. Similarly, for a black 3, there is also only one card: the 3 of clubs.
So, the number of favorable outcomes for a red 2 or a black 3 is 2.
The total possible outcomes remain the same: 52.
Thus, the probability of selecting a red 2 or a black 3 is 2/52, which simplifies to 1/26.
Therefore, your calculation for the probability of selecting a red 2 or a black 3 is incorrect. The correct probability is 1/26, not 1/13.
In summary:
- The probability of selecting a 2 or a 3 is indeed 2/13.
- The probability of selecting a red 2 or a black 3 is 1/26.
Please let me know if you need any further assistance or have any other questions!