Question

Suppose that you are a student worker in the statistics department and agree to be paid by the random pay system. each week the chair flips a coin. if the coin comes up heads, your pay for the week is $80; if it comes up tails, your pay for the week is $40. you work for the department for 100 weeks (at which point you have learned enough probability to know the system is not to your advantage). the probability that , your average earnings in the first two weeks, is greater than $65 is 0.2500. 0.5000. 0.3333.

Answer 1

Answer: PROBABILITY THAT AVERAGE EARNING IN THE FIRST TWO WEEKS IS GREATER THAN $65 = 0.25

Explanation:

GIVEN the following;

Amount paid weekly depends on output of a coin flip:

If HEAD(H) ; $80

else TAIL (T) ; $40

PROBABILITY THAT AVERAGE EARNING IN THE FIRST TWO WEEKS IS GREATER THAN $65:

To obtain an average salary greater than $65;

Consider the following cases:

CASE 1:

First week = T = $40

Second week = T = $40

Average = $80 ÷ 2 = $40 LESS THAN $65

CASE 2:

First week = H = $80

Second week = T = $40

Average = $120 ÷ 2 = $60 LESS THAN $65

The only scenario to obtain an average salary of $65 for the first two weeks is :

First week = H = $80

Second week = H = $80

Average = $80 ÷ 2 = $80 GREATER THAN $65

THEREFORE,

P(H) = required outcome ÷ total possible outcome

P(H) = 0.5

Independent probability:

First week × second week

P(H) × P(H) = 0.5 × 0.5 = 0.25