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Andru [333]
3 years ago
7

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?
Mathematics
1 answer:
Mariana [72]3 years ago
3 0

\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}

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