A game involves selecting a card from a regular 52-card deck and tossing a coin. The coin is a fair coin and is equally likely to land on heads or tails. You pay $3 to play each round. The random variable X is the Net Earnings when you play the game. • If the card is a Face card, and the coin lands on Heads, you win $9. • If the card is a Face card, and the coin lands on Tails, you win $6. • If the card is not a Face card, you win nothing, no matter what the coin shows. a. How can you find the probability of the value of X = when a Face card is chosen from the deck and a Heads is tossed on the coin?

Answer:Expected net earning X for this case is [tex]\frac{18}{26}[/tex] =$0.6923Step-by-step explanation:We need to calculate the probability of the case and multiply by the net earning. The Case is:the card is a Face card, and the coin lands on Heads:Net earning = 9-3 =6 There are 12 Face Cards in a regular 52-card deck. Then,Probability  of a Face Card= [tex]\frac{12}{52}[/tex]Probability that the coin lands on Tails = [tex]\frac{1}{2}[/tex]Then total probability of the case is = [tex]\frac{12}{52}[/tex] × [tex]\frac{1}{2}[/tex] =[tex]\frac{3}{26}[/tex]Expected net earning X for this case is = [tex]\frac{3}{26}[/tex] × 6 = [tex]\frac{18}{26}[/tex]