1st prize-10$, probability of winning this 0.2, 2nd prize-5$, probability of winning 2nd 0.3. Probability distribution of X? Mean amount per week?

Question

I solved this question, however, I'm not sure about the result, so I'd like to see how you solved it. Thank you in advance!

 

Linda takes part in a spelling competition in which first prize is $10 and the second prize $5. The probability that she wins is 0.2, and the probability that she will come second is 0.3. 

A) write out probability distribution of X, the amount Linda wins. 

B) if Linda takes part every week, find the mean amount she wins every week. 

C) one week the entry fee is increased from $3 to $4. Should Linda continue to enter the competition? 

Answer 1

Hi Xenia,

Linda takes part in a spelling competition in which first prize is $10 and the second prize $5. The probability that she wins is 0.2, and the probability that she will come second is 0.3.
A) write out probability distribution of X, the amount Linda wins.
B) if Linda takes part every week, find the mean amount she wins every week.
C) one week the entry fee is increased from $3 to $4. Should Linda continue to enter the competition?

 

Part A)

 

X       10    5       Doesn't win $0

P(X)   .2     .3         .5            

 

NOTE:  In the table the sum of all the probabilities MUST equal 1.   

 

Part B)

To find the mean multiply the probability and the amount

 

10(.2)+5(.3)+0(.5)=

2+1.5+0=

3.5        $3.50 is the mean amount she wins each week

 

C) one week the entry fee is increased from $3 to $4. Should Linda continue to enter the competition?

 

Probably not.  She can only expect to win $3.50.  So if she spends $4 just to play, she is very likely to lose money.

 

Hope this helps you.