Question

You spin the spinner twice what is the probability of landing in a number greater than 5 and then landing on a 3

Answer 1

To determine the probability of landing on a number greater than 5 and then landing on a 3 when spinning a spinner, we first need to clarify the structure of the spinner. Let's assume the spinner is numbered from 1 to 10.

1. **Probability of Landing on a Number Greater than 5:**
The numbers greater than 5 in this case are 6, 7, 8, 9, and 10. This gives us 5 favorable outcomes.

The total number of outcomes (if the spinner has the numbers 1 to 10) is 10.

Therefore, the probability of landing on a number greater than 5 is:
\[
P(X > 5) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{5}{10} = \frac{1}{2}
\]

2. **Probability of Landing on a 3:**
The probability of landing on the number 3 is simply 1 out of 10 possible outcomes:
\[
P(X = 3) = \frac{1}{10}
\]

3. **Combined Probability of Both Events:**
Since the spins are independent events, we can multiply the probabilities of the two events occurring:
\[
P(\text{Greater than 5 and then } 3) = P(X > 5) \times P(X = 3)
\]
Thus, we have:
\[
P(\text{Greater than 5 and then } 3) = \left(\frac{1}{2}\right) \times \left(\frac{1}{10}\right) = \frac{1}{20}
\]

Therefore, the probability of landing on a number greater than 5 and then landing on a 3 is \(\frac{1}{20}\).