Problem Solving

Horse Name
Odds of Placing in the top three

The Baron 3/5


Happy Cynic 7/10


California Girl 3/4


Love Song 1/4


Inamorata 1/2



The chart above lists the odds that a horse will place in the top three. As part of a contest, if at least 2 of the horses that a person bets upon finish in the top three, the bettor receives a T-shirt. If Cecilia bets on The Baron, Happy Cynic, and Inamorata, what is the probability that she does not receive a T-shirt?


A) 3/50
B)21/100
C)29/100
D)35/100
E)65/100

probability that cecilia does not receive t-shirt

= only 1 horse finish in top 3

only 1 horse finish in top 3 [we can have 3 cases]

Barron wins, other two lose
3/5*3/10*1/2 = 9/100

Happy Cynic wins, other two lose
7/10*1/2*2/5 = 7/50

Inamorata wins, other two loses
3/10*2/5*1/2 = 3/50

Combine cases = 9/100 + 7/50 + 3/50 = (9+14+6)/100 = 29/100.

OA?

first of all thanks for replying....but it seems you have not read the question prpoperly, it says that only 5 horses are there and 3 will win so the case of all three horses loosing can not be possible......but yeah can you explain me the meaning of 'odds of placing in top three'....i am confused what it means prob of winning or of loosing

Morgoth wrote:probability that cecilia does not receive t-shirt

= only 1 horse finish in top 3

only 1 horse finish in top 3 [we can have 3 cases]

Barron wins, other two lose
3/5*3/10*1/2 = 9/100

Happy Cynic wins, other two lose
7/10*1/2*2/5 = 7/50

Inamorata wins, other two loses
3/10*2/5*1/2 = 3/50

Combine cases = 9/100 + 7/50 + 3/50 = (9+14+6)/100 = 29/100.

OA?

I believe this is correct, except the question stem says the ODDS of a horse placing in the top 3, while the actual question asks for the PROBABILITY.

I think the question is worded poorly, because, for example in poker, if your odds of winning a hand are 2/1, that means the probability is 1/3. Can someone confirm my logic here.

Morgoth wrote:probability that cecilia does not receive t-shirt

= only 1 horse finish in top 3

only 1 horse finish in top 3 [we can have 3 cases]

Barron wins, other two lose
3/5*3/10*1/2 = 9/100

Happy Cynic wins, other two lose
7/10*1/2*2/5 = 7/50

Inamorata wins, other two loses
3/10*2/5*1/2 = 3/50

Combine cases = 9/100 + 7/50 + 3/50 = (9+14+6)/100 = 29/100.

OA?

This question is written incorrectly, I believe. To answer the question above, you'd need to change ODDS into PROBABILITY (two different things). So, for example, the odds of Barron coming in the top 3 are 3:5, however, the probability of Barron coming in the top 3 is 3/8 (you must add the outcomes together).

Therefore the correct answer to this question should be the following:

(1) Barron in top 3, other 2 picks not: 3/8 * 10/17 *2/3= 60/408
+
(2) HC in top 3, other 2 picks not: 5/8 * 7/17 * 2/3 =70/408
+
(3) Imarota in top 3, other 2 picks not: 5/8*10/17*1/3=50/408

answer is: 180/408= 90/204= 45/102

I'm sure an expert will confirm that my answer is correct, and the problem is worded incorrectly... someone please comment.