Question

A deck of cards has 4 suits, with each suit having 13 cards-- Ace through King (52 cards total). Nicolai randomly draws a card. If their first card is a 9 or Club, they win a net profit of $11 (cost included). If they don't, they draw again (and hold onto their first card). If they draw a 9 or club the 2nd time, they win a net profit of $5. If not, they lose a net amount of $9. Write the probability distribution for x Round your probabilities to 4 decimal places. X P(x) What is the expected value of x? Round your answer to 4 decimal places.

Answer 1

from above below is pmf of X:

P(X=11) =P(9 or club) =16/52=0.3078

P(X=5)=P(not on first and on 2nd) =(1-16/52)*(16/52)=0.2130

P(X=-9) =P(none time) =(1-16/52)*(1-16/52)= 0.4793

x	P(x)
11	0.3077
5	0.2130
-9	0.4793

expected value E(x) =ΣxP(x) =11*0.3077+5*0.2130-9*0.4793 =0.1361 (please try 0.1360 if this comes wrong)