A successful launch of an intercontinental ballistic missile
(ICBM) requires three steps: the signal to fire must reach the
missile team, the ignition mechanism must work properly, and the
missile must not explode prematurely. The Department of Defense
estimates that the probability that the signal to fire an ICBM will
reach a missile team is 0.96. For any given missile, the
probability that the ignition mechanism will work is 0.89. For
missiles with operative ignition systems, 15 of every 100 will
explode in the silo or before reaching orbit. Given the command to
fire, what is the probability of a successful launch for any given
missile.