If the probability is 0.54 that stock a will increase in value during the next month and the probability is 0.68 that stock b will increase in value during the next month, what is the greatest possible value for the probability that neither of these two events will occur?

The probability that neither of both stocks increase  is 0,14

Explanation:

The Complement Rule states that the sum of the probabilities of an event and its complement must equal 1.

The data  we have is the probability that Stock A or B increase,  we are looking for the probability that neither occur,  so we have to use the complement of each one.  

Complement of Stock A =1-0.54=0.46

Complement of Stock B =1-0.68=0.32

If we want to know the probability of both events happening we have to multiply both complements.  

Probability that neither of these two events will occur= 0.46 x0.32= 0,1472‬

b is the correct answer

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