Question

Suppose the probability that markets will fall in Tokyo in 2020 is 0.2, the probability that Japan will reach a trade agreement with China is 0.4, and the probability that the 2020 Olympics will be cancelled is 0.6. Assuming the events are independent, what is the probabibility that (a) Markets will rise, a trade agreement is reached, and the olympics are cancelled (b) A trade agreement is not reached, markets fall, and the Olympics are not cancelled.

Answer 1

Let A be the event that market Will fall, B be the event that trade agreement is reach and C be the event that Olympics are canceled.

So, P(A) = 0.2, P(A') = 1-0.2 = 0.8

P(B) = 0.4 , P(B') = 1 - 0.4 = 0.6

P(C) = 0.6, P(C') = 1 - 0.6 = 0.4

It is given that the events are independent,

a)

Markets will rise, a trade agreement is reached, and the olympics are cancelled  

P( A' and B and C) = P(A')*P(B)*P(C)

= 0.8* 0.4* 0.6 = 0.192

b)

A trade agreement is not reached, markets fall, and the Olympics are not cancelled.

P(B' and A and C') =P (B') * P(A) * P(C')

= 0.6 *0.2 * 0.4 = 0.048