Explanation:
we seek the probability of a combination of independent events.
since they are independent, we can simply multiply the 3 individual probabilities.
1. spin an odd number (in our case that means 1 or 3) out of the possible 3. that probabilty is therefore 2/3.
2. flipping head with a coin. so, 1 out of possible 2. that probabilty is therefore 1/2
3. spin yellow. that is 1 out of possible 3. that probabilty is therefore 1/3.
again, none of the single events is influencing the outcome of any of the other 2 events, so, the total probabilty of the combination is the product of the single probabilities :
2/3 × 1/2 × 1/3 = 2/18 = 1/9
FYI : the first single probabilty is actually the result of an "or" relationship of 2 possible results of one event :
the probabilty to get an odd number is the same as the probabilty to get 1 or to get 3. both are non-overlapping possible outcomes of one event, so we can add the individual probabilities for the result.
each possible outcome has the probabilty of 1/3, so the "or" relation has a probabilty of 1/3 + 1/3 = 2/3.