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

`(5)/(24)`

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)`=
`(1)/(2)`

Probability to get a
`4` in the die=
`p_(4)`
`=(1)/(6)`

Probability to get a head and get a 4 in die=[
`p_(1)`tex]p_{head}\times p_{4}[/tex]=
`(1)/(2)* (1)/(6) =(1)/(12)`

Probability to get a tail=
`p_(tail)`=
`(1)/(2)`

Probability to get a heart=
`p_(heart)`=
`(13)/(52) =(1)/(4)`

Probability to get a tail and get a heart in the deck=
`p_(tail) * p_(heart)`=
`(1)/(2)* (1)/(4)=(1)/(8)`

Total probability to win a jackpot=
`p_(1)+p_(2)=(1)/(12)+(1)/(8)=(5)/(24)`

So,probability to win a jackpot is
`(5)/(24)`