Question

let a and b be independent events associated with certain random experiments such that thenprobability of a is 0.25 and the probability of b is 0.5 then what is the probability of aub

Answer 1

Answer:

0.625

Step-by-step explanation:

Two approaches of interest.

First method  ---  inclusion-exclusion

P(a∪b) = P(a) + P(b) - P(a∩b)

         = P(a) + P(b) - P(a)P(b)           [ since a and b are independent ]

         = 0.25 + 0.5 - 0.25×0.5

         = 0.25 + 0.5 - 0.125

         = 0.625

Second method  ---  De Morgan

P(a∪b) = 1 - P( (a∪b)' )                  [ the dash is indicating "complement" ]

         = 1 - P( a' ∩ b' )

         = 1 - P(a')P(b')                   [ since a, b indpendent, so are a' and b' ]

         = 1 - ( 1 - P(a) ) ( 1 - P(b) )

         = 1 - (1 - 0.25) (1 - 0.5)

         = 1 - 0.75 × 0.5

         = 1 - 0.375

         = 0.625