The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.50. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.20 and P(B | A2) = 0.05. If needed, round your answers to three decimal digits. (a) Are A1 and A2 mutually exclusive?

The inclusion-exclusion principle says

P(A1 ∩ A2) = P(A1) + P(A2) - P(A1 ∪ A2)

We know the probability of intersection is 0, so

P(A1) + P(A2) = P(A1 ∪ A2)

which means A1 and A2 are indeed mutually exclusive.

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

1/3

step-by-step explanation:

to find this, you can divide 12 by 4 which is 3 or you can multiply 4 until you reach 12 (4x3=12). both should give you 3, meaning theres three times less bananas than there are oranges.