Hi,
Can someone please help me with the following question? ---
Alice and Bob can go to the market once on either of the following days -- Tuesday...Saturday. What is the probability of them having gone to the market on consecutive days?
I am getting a 4/5. But the answer is 8/25. How come?
Thanks.
Shilo
Probability --Consecutive days
This topic has expert replies
GMAT/MBA Expert
- Ian Stewart
- GMAT Instructor
- Posts: 2621
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
4/5 is the probability they went to the market on different days, so the probability they went on consecutive days must be smaller than 4/5.
You might consider cases: either Alice went at the beginning/end of the week, or Alice went in the middle of the week. We can then work out the probabilities of each, and add, using the 'or' rule for probability:
The probability that Alice went on Tuesday or Saturday is 2/5. Then there's only a 1/5 chance that Bob went on the day before or after Alice:(2/5)*(1/5) = 2/25.
The probability that Alice went on W, Th, or F is 3/5. In each case, the probability is 2/5 that Bob went the day before or after Alice. (3/5)*(2/5) = 6/25.
2/25 + 6/25 = 8/25
You might consider cases: either Alice went at the beginning/end of the week, or Alice went in the middle of the week. We can then work out the probabilities of each, and add, using the 'or' rule for probability:
The probability that Alice went on Tuesday or Saturday is 2/5. Then there's only a 1/5 chance that Bob went on the day before or after Alice:(2/5)*(1/5) = 2/25.
The probability that Alice went on W, Th, or F is 3/5. In each case, the probability is 2/5 that Bob went the day before or after Alice. (3/5)*(2/5) = 6/25.
2/25 + 6/25 = 8/25
-
- Junior | Next Rank: 30 Posts
- Posts: 11
- Joined: Wed Aug 13, 2008 7:31 am
- Thanked: 4 times
1/5 probability that Alice goes to market on Tuesday .
1/5 probability that Bob goes to market on Wednesday .
So probability that Alice goes to market on Tuesday and Bob goes to market on Wednesday = 1/5 * 1/5 = 1/25
Similarly for the next 3 days the probabilities will be 1/25 each.
So probability that Alice and Bob go to market on consecutive days but Alice goes first = 1/25 + 1/25 + 1/25 + 1/25 = 4/25
Similarly probability that Bob and Alice go to market on consecutive days but Bob goes first = 4/25
Total probability that they go on consecutive days = 4/25 + 4/25 = 8/25.
Sorry the response is late but nevertheless can be useful.
1/5 probability that Bob goes to market on Wednesday .
So probability that Alice goes to market on Tuesday and Bob goes to market on Wednesday = 1/5 * 1/5 = 1/25
Similarly for the next 3 days the probabilities will be 1/25 each.
So probability that Alice and Bob go to market on consecutive days but Alice goes first = 1/25 + 1/25 + 1/25 + 1/25 = 4/25
Similarly probability that Bob and Alice go to market on consecutive days but Bob goes first = 4/25
Total probability that they go on consecutive days = 4/25 + 4/25 = 8/25.
Sorry the response is late but nevertheless can be useful.
-
- Master | Next Rank: 500 Posts
- Posts: 152
- Joined: Wed Mar 12, 2008 4:36 pm
- Thanked: 8 times
- Followed by:2 members