If the spinner is spun twice, what is the probability that it will stop on an odd number both times?
1/42
To find the probability of two independent events both happening, you multiply the probabilities of each event.
Assuming that the spinner has an equal chance of landing on any number, and there are six numbers (1, 2, 3, 4, 5, 6), there are three odd numbers (1, 3, 5) and three even numbers (2, 4, 6).
The probability of the spinner stopping on an odd number in a single spin is 3/6, or 1/2.
Since the two spins are independent events, the probability of the spinner stopping on an odd number both times is (1/2) * (1/2) = 1/4.
Therefore, the probability that the spinner will stop on an odd number both times is 1/4.
To find the probability that the spinner will stop on an odd number both times when spun twice, we need to know the total number of possible outcomes and the number of favorable outcomes.
Let's break it down step by step:
Step 1: Determine the total number of outcomes.
Assuming the spinner has numbers 1 to 6, there are six equally likely outcomes when the spinner is spun once. Since the spinner is spun twice, the total number of outcomes will be 6 * 6 = 36.
Step 2: Determine the number of favorable outcomes.
For the spinner to stop on an odd number both times, we need to consider the possible outcomes. The odd numbers on the spinner are 1, 3, and 5. So, we need to find the favorable outcomes where the spinner stops on any of these odd numbers twice.
Since we have three odd numbers, the number of favorable outcomes would be 3 * 3 = 9.
Step 3: Calculate the probability.
To calculate the probability, we divide the number of favorable outcomes by the total number of outcomes:
Probability = Number of favorable outcomes / Total number of outcomes.
Plugging in the numbers, we get:
Probability = 9 / 36 = 1/4 = 0.25.
Therefore, the probability that the spinner will stop on an odd number both times when spun twice is 0.25 or 1/4.