The genetic origin and properties of maize (modern-day corn) was investigated in Economic Botany (Jan.–Mar. 1995). Seeds from maize ears carry either single spikelets or paired spikelets, but not both. Progeny tests on approximately 600 maize ears revealed the following information. Forty percent of all seeds carry single spikelets, and 60% carry paired spikelets. A seed with single spikelets will produce maize ears with single spikelets 29% of the time and paired spikelets 71% of the time. A seed with paired spikelets will produce maize ears with single spikelets 26% of the time and paired spikelets 74% of the time.
a. Find the probability that a randomly selected maize ear seed carries a single spikelet and produces ears with single spikelets.
b. Find the probability that a randomly selected maize ear seed produces ears with paired spikelets.