Question
You pick a card at random. Without putting the first card back, you pick a second card at random.
1
2
3
4
5
6
What is the probability of picking an odd number and then picking an odd number?
Write your answer as a percentage.
%
1
2
3
4
5
6
What is the probability of picking an odd number and then picking an odd number?
Write your answer as a percentage.
%
Answers
GPT-4o mini
To solve the problem, we first identify the odd and even numbers in the set of cards:
The cards are: 1, 2, 3, 4, 5, 6.
The odd numbers in this set are: 1, 3, 5.
So there are 3 odd numbers out of a total of 6 cards.
**Step 1: Probability of picking an odd number first**
The probability of picking an odd number on the first draw is:
\[
P(\text{odd first}) = \frac{\text{Number of odd numbers}}{\text{Total number of cards}} = \frac{3}{6} = \frac{1}{2}
\]
**Step 2: Probability of picking an odd number second, given the first was odd**
If the first card drawn is odd, there will be now 2 odd cards left and 5 cards total left (since we do not put the card back).
The probability of picking an odd number on the second draw is:
\[
P(\text{odd second | odd first}) = \frac{\text{Remaining odd numbers}}{\text{Total remaining cards}} = \frac{2}{5}
\]
**Step 3: Total probability of both events occurring**
To find the total probability of both events (picking an odd number first and then picking another odd number), we multiply the probabilities of the two independent events:
\[
P(\text{odd first and odd second}) = P(\text{odd first}) \times P(\text{odd second | odd first}) = \frac{1}{2} \times \frac{2}{5} = \frac{2}{10} = \frac{1}{5}
\]
**Step 4: Convert to percentage**
To convert the probability to a percentage, we multiply by 100:
\[
\frac{1}{5} \times 100 = 20\%
\]
Thus, the probability of picking an odd number and then picking an odd number is \(\boxed{20\%}\).
The cards are: 1, 2, 3, 4, 5, 6.
The odd numbers in this set are: 1, 3, 5.
So there are 3 odd numbers out of a total of 6 cards.
**Step 1: Probability of picking an odd number first**
The probability of picking an odd number on the first draw is:
\[
P(\text{odd first}) = \frac{\text{Number of odd numbers}}{\text{Total number of cards}} = \frac{3}{6} = \frac{1}{2}
\]
**Step 2: Probability of picking an odd number second, given the first was odd**
If the first card drawn is odd, there will be now 2 odd cards left and 5 cards total left (since we do not put the card back).
The probability of picking an odd number on the second draw is:
\[
P(\text{odd second | odd first}) = \frac{\text{Remaining odd numbers}}{\text{Total remaining cards}} = \frac{2}{5}
\]
**Step 3: Total probability of both events occurring**
To find the total probability of both events (picking an odd number first and then picking another odd number), we multiply the probabilities of the two independent events:
\[
P(\text{odd first and odd second}) = P(\text{odd first}) \times P(\text{odd second | odd first}) = \frac{1}{2} \times \frac{2}{5} = \frac{2}{10} = \frac{1}{5}
\]
**Step 4: Convert to percentage**
To convert the probability to a percentage, we multiply by 100:
\[
\frac{1}{5} \times 100 = 20\%
\]
Thus, the probability of picking an odd number and then picking an odd number is \(\boxed{20\%}\).