Final answer:
The probability of the outcome (black, white, red) is 1/36. This is found by first calculating the probability of landing on white (1/6) and then applying the product rule to the probabilities of landing on black (1/2), white (1/6), and red (1/3).
Step-by-step explanation:
To find the probability of getting the outcome (black, white, red) when the spinner is spun three times, we need to consider the probabilities of each event independently and then apply the product rule for independent events.
The probability of landing on black is given as 1/2, the probability of landing on white is not directly given but can be found since we have the probabilities for black and red. The probability of the entire spinner outcomes should sum up to 1, so if we subtract the probability of black (1/2) and red (1/3) from 1, we get the probability of landing on white.
Calculating the probability of white:
P(white) = 1 - P(black) - P(red) = 1 - 1/2 - 1/3 = 1/6.
Now we use the product rule to calculate the desired outcome:
P(black, white, red) = P(black) x P(white) x P(red) = (1/2) x (1/6) x (1/3) = 1/36.
Therefore, the probability of the spinner landing on black, then white, then red in three spins is 1/36, which corresponds to the answer option b. 1/36.