Cameron flips two coins and then spins the spinner below. What is the probability of having two different outcomes on the coins and spinning an odd number?A. 1/16B. 1/8C. 1/4D. 1/2the numbers on the spinner are 1, 2, 3, and 4.

Accepted Solution

Answer:C: 1/4Step-by-step explanation:We have tow events: flipping the coin and spinning the number. As both are independent -there are no reason to expect that the result of the coin affect the spinning or vice-versa- we can treat the probabilities as independents. First, lets get the probability of flipping two coins and get different outcomes.If we flip 2 coins our universe is not big. Our possible outcomes are (face is F and tail is T):F F, F T, T F, T TSo, we have 4 possible outcomes. Which of these we want? Only 2: F T and T F. As we only want 2 from 4, the probability of having different outcomes , and each of them has an equal probability of 1/4:P(diff outcomes) = P (F T or T F) = 1/4 + 1/4 = 1/2So, the probability of different outcomes is 1/2. Then we need to get the probability of having an odd number from the spinning, and it is really similar to the coin event. Our universe is: 1, 2, 3, 4from these, only two numbers are odd:1 and 3As any of them has the same probability of 1/4, the probability of odd number is:P(odd) = P (1 or 3) = 1/4 + 1/4 = 1/2So, as both events have a probability if 1/2 and are independent:P(diff outcomes AND odd) =  P(different outcomes) * P(odd) = 1/2 * 1/2 = 1/4Option C