Question

lnacertain tom, 6 % of hoseholds own a cell phone, sos have h ghspeed Internet and 30% have both a cell-phone and high oa. 10% peed internet. The proportion of hoses that have neither acea phone nor high speed htme is @e.. This is impossible, as the values add up to more than ข00%

Answer 1

Answer

Let us define variable for Cell phone and high speed internet, i.e. CP for cell phone and HSI for high speed internet.

	HSI	HSI(complement)
CP	0.30	=0.6-0.3 = 0.30
CP(complement)	=0.5-0.3 = 0.20	1-(0.3+0.3+0.2)= 0.20

Now, we know that 60% or 60/100 = 0.60 has CP

50% or 50/100 = 0.50 has HSI

and 30% or 30/100 = 0.30 has both

CP and HSI denote denote both, which is equal to 0.30

CP and HSI complement = CP - (CP and HSI) = 0.6- 0.3 = 0.3

Similarly, CP(complement) and HSI = HSI - (Cp and HSI) = 0.50-0.30 = 0.20

Now, we have to find complement of CP and HSI

we know that the sum of all probabilities must be equal to 1.

So, we can write complement of CP and HSI = 1 - (all given probability in table) = 1-(0.30+0.30+0.20) = 1 - 0.80 = 0.20

So, we can write 0.20*100 = 20%

Correct answer is option C