In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a three. You pick a card from a full playing-card deck, and success would be picking a ace with heart card.
If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
Pick one.
A) 61/312  B) 13/624  C) 325/624  D) 181/312  E) 163/625
Event(1): Probability of getting head in a flip of coin = 1/2   Event(2): Probability of getting three in a roll of dice = 1/6   Event(3): Probability of getting ace with heart in a pack of card = 1/52   Probability of winning is having exactly one successful event is:   P(success 1)* P(Fail 2)* P(Fail 3) + P(Fail 1)* P(Success 2)* P(Fail 3) + P(Fail 1)* P(Fail 2)* P(Success 3)   = 1/2*5/6*51/52 +1/2*1/6*51/52 +1/2*5/6*1/52   =255/624 + 102/624 +5/624   =362/624   = 181/312   Answer :181/312
<result>D</result>
In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a three. You pick a card from a full playing-card deck, and success would be picking a ace with heart card.
If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?