Question

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?

Answer 1

$\frac{5}{24}$

Step-by-step explanation:

There are two ways to win a jackpot.

Let $p_{1}$ be the probability for first method and $p_{2}$ be the probability for second method.

Probability to get a head=$p_{head}$=$\frac{1}{2}$

Probability to get a $4$ in the die=$p_{4}$$=\frac{1}{6}$

Probability to get a head and get a 4 in die=[$p_{1}$tex]p_{head}\times p_{4}[/tex]=$\frac{1}{2}\times \frac{1}{6} =\frac{1}{12}$

Probability to get a tail=$p_{tail}$=$\frac{1}{2}$

Probability to get a heart=$p_{heart}$=$\frac{13}{52} =\frac{1}{4}$

Probability to get a tail and get a heart in the deck=$p_{tail} \times p_{heart}$=$\frac{1}{2}\times \frac{1}{4}=\frac{1}{8}$

Total probability to win a jackpot=$p_{1}+p_{2}=\frac{1}{12}+\frac{1}{8}=\frac{5}{24}$

So,probability to win a jackpot is $\frac{5}{24}$