Dust explosions in the chemical process industry, although rare, pose a great potential for injury and equipment damage. Process Safety Progress (Sept., 2004) reported on the likelihood of dust explosion incidents. The table gives the proportion of incidents in each of several worldwide industries where dust explosions have occurred. Suppose 20 dust explosions occur worldwide next year.

a. Find the probability that 7 explosions occur in the wood/paper industry, 5 occur in the grain/foodstuffs industry, 2 occur in the metal industry, none occur in the power industry, 1 occurs in the plastics/mining/ textile industry, and 5 occur in all other industries.
b. Find the probability that fewer than 3 occur in the wood/paper industry.

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Industry Proportion Wood/Paper 30 Grain/Foodstuffs .10 Metal .07 Power Generation .07 Plastics/Mining/Textile .08 Miscellaneous 38