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?

Exercise: counting committees 0.0/2.0 puntos (calificable) we start with a pool of n people. a chaired committee consists of k≥1 members, out of whom one member is designated as the chairperson. the expression k(nk) can be interpreted as the number of possible chaired committees with k members. this is because we have (nk) choices for the k members, and once the members are chosen, there are then k choices for the chairperson. thus, c=∑k=1nk(nk) is the total number of possible chaired committees of any size. find the value of c (as a function of n ) by thinking about a different way of forming a chaired committee: first choose the chairperson, then choose the other members of the committee. the answer is of the form c=(α+nβ)2γn+δ. what are the values of α , β , γ , and δ ?