Question

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 1

Answer:

Expected net earning X for this case is $\frac{18}{26}$ =$0.6923

Step-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= $\frac{12}{52}$

Probability that the coin lands on Tails = $\frac{1}{2}$

Then total probability of the case is = $\frac{12}{52}$ × $\frac{1}{2}$ =$\frac{3}{26}$

Expected net earning X for this case is = $\frac{3}{26}$ × 6 = $\frac{18}{26}$