Of all the weld failures in a certain assembly in the past, 85% of them occur in the weld metal itself, 10% occur in the base metal, and the cause is unknown in 5% of failures. A sample of 10 weld failures from a specific welder is examined. Assuming the failure rates given above apply to this welder's welds,

(a) What is the probability that exactly six of the failures are weld metal failures?

(b) What is the probability that fewer than 2 of the failures are base metal failures?

(c) What is the probability that at least one of the failures have unknown cause?