In a certain game, you perform three tasks. You flip a quarter, and

MAGOOSH OFFICIAL SOLUTION:

This is very tricky. We have to think of three cases.

Case One: success with coin, no success with die or card
P(coin = H AND die ≠ 6 AND card ≠ spade) = (1/2)*(5/6)*(3/4) = 15/48

Case Two: success with die, no success with coin or card
P(coin = T AND die = 6 AND card ≠ spade) = (1/2)*(1/6)*(3/4) = 3/48

Case Three: success with card, no success with die or coin
P(coin = T AND die ≠ 6 AND card = spade) = (1/2)*(5/6)*(1/4) = 5/48

The winning scenario could be Case One OR Case Two OR Case Three. Since these are joined by OR statements and are mutually exclusive, we simply add the probabilities.

P(win game) = 15/48 + 3/49 + 5/48 = 23/48.

Answer = (E)

Event(1): Probability of getting head in a flip of coin = 1/2
Event(2): Probability of getting 6 in a roll of dice = 1/6
Event(3): Probability of getting spade in a pack of card = 1/4

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*3/4 +1/2*1/6*3/4 +1/2*5/6*1/4
=15/48 + 3/48 +5/48
=23/48

E

Not a realistic GMAT question, because you don't need to know about decks of cards for the test, but we have:

chance of 'success' with the coin: 1/2
chance of 'success' with the die: 1/6
chance of 'success' with the card: 1/4

There are three ways to win. One way: we might succeed with the coin *and* fail with the die *and* fail with the card. To find the probability that happens, we multiply each individual probability: (1/2)(5/6)(3/4)

But we might succeed with the die and fail with the other items: (1/2)(1/6)(3/4)

Or we might succeed with the card and fail with the other items: (1/2)(5/6)(1/4)

Adding the probabilities from those three cases gives the answer:

(1/2)(5/6)(3/4) + (1/2)(1/6)(3/4) + (1/2)(5/6)(1/4) = 23/(2)(6)(4) = 23/48

Is it possible to do this question by 1 - [probability of losing every task]?

It anyways signifies, any one task turning to be favorable. I tried doing this way, but ended up getting 11/16 and chose the wrong answer D. What am I missing?