Question

Given that p(a) = 0.23, p(b) = 0.50, and p(a and b) = 0.12, what is the probability of the union of events a and b?

1) 0.35
2) 0.61
3) 0.73
4) 0.85

Answer 1

The probability of the union of events a and b is calculated using the formula P(a OR b) = P(a) + P(b) - P(a AND b), which gives us 0.61.

Step-by-step explanation:

To find the probability of the union of events a and b, denoted as P(a OR b), we use the formula:

P(a OR b) = P(a) + P(b) - P(a AND b)

Substituting the given probabilities into the formula:

P(a OR b) = 0.23 + 0.50 - 0.12

P(a OR b) = 0.73 - 0.12

P(a OR b) = 0.61

Therefore, the probability of the union of events a and b is 0.61, which corresponds to option 2). This computation, based on the inclusion-exclusion principle, accounts for the probabilities of both events while adjusting for their intersection, elucidating the likelihood of either a or b occurring, essential in various statistical and decision-making contexts.