Probability --Consecutive days

[shilotilo]

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

[Ian Stewart]

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

[shilotilo]

Thanks Ian




Shilo

[gmatters2vj]

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.

[artistocrat]

There is a simpler solution:

There are 5X5 possibilities...write that 25 on the bottom (denominator).

The numerator can include TW, WT, TF, FS for the 2 of them that's 8 (numerator)

8/25