Agame 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?

Expected net earning X for this case is =$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=

Probability that the coin lands on Tails =

Then total probability of the case is = × =

Expected net earning X for this case is = × 6 =

associative property of multiplication

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.