You pick a card at random, put it back, and then pick another card at random.



5

6

7


What is the probability of picking a number greater than 5 and then picking a 7?

*Write your answer as a percentage rounded to the nearest tenth.*

To find the probability of picking a number greater than 5 followed by picking a 7, we can solve this step by step:

### Step 1: Determine the probability of picking a number greater than 5.
From the list of numbers: 5, 6, and 7, the numbers greater than 5 are 6 and 7. There are 2 such numbers (6 and 7) out of 3 total numbers.

\[
P(\text{greater than 5}) = \frac{2}{3}
\]

### Step 2: Determine the probability of picking a 7 after putting the card back.
Since we put the card back, the probability of picking a 7 is still \(\frac{1}{3}\), as there is 1 "7" out of 3 cards.

\[
P(\text{picking a 7}) = \frac{1}{3}
\]

### Step 3: Calculate the combined probability.
Since these are independent events, we multiply the two probabilities:

\[
P(\text{greater than 5 and then picking a 7}) = \frac{2}{3} \times \frac{1}{3} = \frac{2}{9}
\]

### Step 4: Convert the result to a percentage.
To express this probability as a percentage, we multiply by 100:

\[
\frac{2}{9} \times 100 = 22.2222\%
\]

### Step 5: Round to the nearest tenth.
Rounding 22.2222% to the nearest tenth gives:

\[
22.2\%
\]

Thus, the probability is **22.2%**.

Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:
1. What is the probability of picking two 7s in a row?
2. If the card is not replaced, how would the probabilities change?
3. What is the probability of picking a number less than 7 both times?
4. How does the probability change if we add an extra card with the number 8?
5. How would you calculate the probability of picking any specific number twice in a row?

**Tip:** In independent events, probabilities multiply, while in mutually exclusive events, they add!

You pick a card at random, put it back, and then pick another card at random. What is the probability of picking a number greater than 5 and then picking a 7? Write your answer as a percentage rounded to the nearest tenth.

Learn how to calculate the probability of picking a number greater than 5 followed by a 7 when selecting random cards. This step-by-step guide covers essential probability concepts and includes key formulas, suitable for students in Grades 6-8.

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