For the given decision algorithm find how many outcomes are

For the given decision algorithm, find how many outcomes are possible. HINT [See Example 1.] Step 1: Step 2: Alternative 1: 1 outcome Alternative 1: 4 outcomes Alternative 2: 3 outcomes Alternative 2: 4 outcomes Alternative 3: 1 outcome

Solution

step 1 :

alternative 1 : 1 outcome

alternative 2 : 3 outcomes

alternative 1 : 1 outcome

step 2 :

alternative 1 : 4 outcomes

alternative 2 : 4 outcomes

total number of possible outcomes = we\'ll have to form cases of outcomes amongst the two seps

like alternative 1 from step 1 has 1 outcome and it can combine with the first alternative of step 2 in 4 different ways as there are 4 outcomes in alternative 1 from step 2

=> likewise alternative 1 from step 1 forms 4 outcomes with the alternative 2 of step 2

similarly alternative 2 of step 1 can for 3*4 = 12 outcomes with alternative 1 from step 2 ,

likewise with alternative 2 of step 2 = 12 outcomes

alternative 3 of step 1 forms 4 outcomes with alternative 1 of step 2

and another 4 outcomes with slternative 2 of step 2

hence the total number of possible outcomes = 4 + 4 + 12 + 12 + 4 + 4 = 40 outcomes