Dear all,
although i solved the below probability problem in 2 different ways using probability and combinations, i was wondering if there is any way easier and shorter than mine because each time i solved it took me more than 2 minutes doing many calculations. please let me know if there is a shortcut so solving it without doing many calculations.
7. In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won? What is the probability that one will have at least three draws before one picks a heart?
A. 1/2
B. 9/16
C. 11/16
D. 13/16
E. 15/16
Here is how I did it:
Probability:
number of different possibilities: 52 x 52 x 52 = 52^3
break rule: 39/52 x 39/52 x 39/52 = 39^3/52^3 --> here it took me so long to do calculations
1 - break: 52^3/52^3 - 39^3/52^3 --> also here it took a lot of time to do calculations to arrive to the right answer choice
Combinations:
Ignore rule: 52 x 52 x 52 = 52^3
break rule: 39 x 39 x 39
(ignore - break)/ignore = (52^3 - 39^3)/52^3
although i solved the below probability problem in 2 different ways using probability and combinations, i was wondering if there is any way easier and shorter than mine because each time i solved it took me more than 2 minutes doing many calculations. please let me know if there is a shortcut so solving it without doing many calculations.
7. In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won? What is the probability that one will have at least three draws before one picks a heart?
A. 1/2
B. 9/16
C. 11/16
D. 13/16
E. 15/16
Here is how I did it:
Probability:
number of different possibilities: 52 x 52 x 52 = 52^3
break rule: 39/52 x 39/52 x 39/52 = 39^3/52^3 --> here it took me so long to do calculations
1 - break: 52^3/52^3 - 39^3/52^3 --> also here it took a lot of time to do calculations to arrive to the right answer choice
Combinations:
Ignore rule: 52 x 52 x 52 = 52^3
break rule: 39 x 39 x 39
(ignore - break)/ignore = (52^3 - 39^3)/52^3
