Suppose nine school children line up to board a school has T

Suppose nine school children line up to board a school has. There are 4 girls and 5 boys. What is the number of ways they could line up: Without any restriction So that 4 girls are first then 5 boys in the line. How many 5-letter words can be made from the word: \"SUPER\" ? How many 11-letter words can be made from the word: \"MATHEMATICS\"? Three machines I, II and III manufacture 0.4,0.5 and 0.1 of the total production in a plant, respectively. The percentage of defective items produced by I, II and III is 2%, 4% and 1% respectively. Construct the tree diagram For an item chosen at random. What is the probability that it is defective? What is the probability that the defective item came from machine I?

Solution

7 )

a) 9 students to arrange

no ofways = 9!

b) 4 girls are first then 5 boys,

no of ways = 4! ( to arrange girls) * 5! (to arrange boys)

8) b) no of 11 letter words (2M 2A 2T I C S H E

11!/(2!2!2!)

9)

prob(defective) = 0.4 * 0.02 + 0.5 * 0.04 + 0.1 * 0.01 = 0.029

Use Baye\'s theorem

given its defective P(machine1) = 0.4 * 0.02/ 0.029