A telemarketer has probability 01 of selling an air filter d

A telemarketer has probability 0.1 of selling an air filter during any given phonecall. If the telemarketer makes 14 independent calls, what\'s the probability he\'ll make more than two sales?

Solution

p(more than two sales) = 1- p(0 sales) - p(1 sale) - p( 2 sale)

= 1- 0.9¹⁴ - 0.9¹³X0.1 - 0.9¹²X0.1X0.1

= 1- 0.9¹⁴ - 0.9¹²X0.1(0.9-0.1)

= 1- 0.9¹⁴ - 0.9¹²X0.1X0.8

= 1-0.9¹²(0.9X0.9-0.1X0.8)

= 1- 0.9¹²X0.73

= 1-0.206

= 0.794