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?

Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. when the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. when the tanks are completely full of air, the submarine reduces its overall mass and floats to the surface. depending on the density of the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. the volume of the submarine never changes. when the tanks are completely full of water, a submarine with a volume of 7.8\times10^3\text{ m}^37.8×10 3 m 3 7, point, 8, times, 10, start superscript, 3, end superscript, space, m, start superscript, 3, end superscript has a total mass of 8\times10^6\text{ kg}8×10 6 kg8, times, 10, start superscript, 6, end superscript, space, k, g. the density of the seawater is 10^3\text{ kg/m}^310 3 kg/m 3 10, start superscript, 3, end superscript, space, k, g, slash, m, start superscript, 3, end superscript. to make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?