Question

The probability that a rose flowers in Spring is ( 6/10 ) and that a rose flowers in Summer is ( 0.5 ). A rose never flowers in the Winter. What is the probability it flowers in Autumn?

a) ( 1/5 )
b) ( 2/5 )
c) ( 3/10 )
d) ( 1/2 )

Answer 1

Based on the provided probabilities for Spring, Summer, and Winter, the question seems to include a mistake as the total exceeds 100%. Probabilities for separate exclusive events should sum up to 1 or less. Without the correct probabilities, finding the accurate probability for Autumn is not possible.

Step-by-step explanation:

To find the probability that a rose flowers in Autumn, you would need to know the probabilities for Spring, Summer, Autumn, and Winter. Given that the probability for Spring is (6/10) or 60%, for Summer it is (0.5) or 50%, and for Winter it is 0% because a rose never flowers in Winter, we can deduce the probability for Autumn.

Since probabilities must add up to 100% or 1 for the complete set of all possible outcomes (Spring, Summer, Autumn, and Winter), we can write an equation to solve for the probability of Autumn:

Probability(Autumn) = 1 - (Probability(Spring) + Probability(Summer) + Probability(Winter))

Probability(Autumn) = 1 - (0.6 + 0.5 + 0.0)

Probability(Autumn) = 1 - 1.1

Which does not make sense because probabilities cannot be negative and the total probability exceeds 1, indicating that there is an error in the given probabilities or an underlying assumption. In real-world scenarios, the probabilities for separate events (like flowering in different seasons for a plant) should always add up to 1 or less. Therefore, it's possible that the probabilities provided are conditional or there's additional context needed to solve this properly.