The spinner below is spun twice. If the spinner lands on a border, that spin does not count and spin again. It is equally likely that the spinner will land in each of the six sectors.
For each question below, enter your response as a reduced fraction.
Find the probability of spinning cyan on the first spin and red on the second spin.
Find the probability of spinning blue on the first spin and red on the second spin.
Find the probability of NOT spinning blue on either spin. (Not blue on the first spin and not blue on the second spin.)
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Final Answer: The probability of spinning cyan on the first spin and red on the second spin is \(\boxed{\frac{1}{36}}\). The probability of spinning blue on the first spin and red on the second spin is \(\boxed{\frac{1}{36}}\). The probability of NOT spinning blue on either spin is \(\boxed{\frac{25}{36}}\).
Step 1 ：The spinner has six sectors, and it is equally likely that the spinner will land in each of the six sectors. Therefore, the probability of landing on a specific color is \(\frac{1}{6}\).
Step 2 ：For the first question, we need to find the probability of spinning cyan on the first spin and red on the second spin. Since the two spins are independent events, the probability of both events happening is the product of their individual probabilities. Therefore, the probability of spinning cyan on the first spin and red on the second spin is \(\frac{1}{6} \times \frac{1}{6} = \frac{1}{36}\).
Step 3 ：For the second question, we need to find the probability of spinning blue on the first spin and red on the second spin. The reasoning is the same as for the first question. Therefore, the probability of spinning blue on the first spin and red on the second spin is \(\frac{1}{6} \times \frac{1}{6} = \frac{1}{36}\).
Step 4 ：For the third question, we need to find the probability of NOT spinning blue on either spin. This means that the spinner must land on one of the other five colors on both spins. The probability of not landing on blue on a single spin is \(\frac{5}{6}\), and since the two spins are independent, the probability of not landing on blue on either spin is \(\left(\frac{5}{6}\right)^2 = \frac{25}{36}\).
Step 5 ：Final Answer: The probability of spinning cyan on the first spin and red on the second spin is \(\boxed{\frac{1}{36}}\). The probability of spinning blue on the first spin and red on the second spin is \(\boxed{\frac{1}{36}}\). The probability of NOT spinning blue on either spin is \(\boxed{\frac{25}{36}}\).
