A game starts by flipping a coin. If you get heads, then you get to roll a die and, if you roll a 4, you win the jackpot. If you get tails, you must pick a card from a deck and, if you get a heart, you win the jackpot. What is the probability of winning the jackpot in this game?

[tex]\frac{5}{24}[/tex]Step-by-step explanation:There are two ways to win a jackpot.Let [tex]p_{1}[/tex] be the probability for first method and [tex]p_{2}[/tex] be the probability for second method.Probability to get a head=[tex]p_{head}[/tex]=[tex]\frac{1}{2}[/tex]Probability to get a [tex]4[/tex] in the die=[tex]p_{4}[/tex][tex]=\frac{1}{6}[/tex]Probability to get a head and get a 4 in die=[[tex]p_{1}[/tex]tex]p_{head}\times p_{4}[/tex]=[tex]\frac{1}{2}\times \frac{1}{6} =\frac{1}{12}[/tex]Probability to get a tail=[tex]p_{tail}[/tex]=[tex]\frac{1}{2}[/tex]Probability to get a heart=[tex]p_{heart}[/tex]=[tex]\frac{13}{52} =\frac{1}{4}[/tex]Probability to get a tail and get a heart in the deck=[tex]p_{tail} \times p_{heart}[/tex]=[tex]\frac{1}{2}\times \frac{1}{4}=\frac{1}{8}[/tex]Total probability to win a jackpot=[tex]p_{1}+p_{2}=\frac{1}{12}+\frac{1}{8}=\frac{5}{24}[/tex]So,probability to win a jackpot is [tex]\frac{5}{24}[/tex]