Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
The daily change in CF Corp’s stock price can be compared to a coin flip. Heads – the price goes up by $1. Tails – the price goes down by $1. Moreover, the coin is “fair”: that is, each daily outcome is equally possible (meaning that the chance of heads is 50%, and the chance of tails is 50%). This also means that any particular sequence of flips is equally probable. As a result, our probability calculation is simplified. We just count the 5-day sequences that give us a $3 increase, then we compare that number to the total number of 5-day sequences.
To go up exactly $3, we need exactly 4 “up” days (heads) and 1 “down” day (tails). We don’t care about the order in which these days come. So we need to count the possible arrangements of 4 heads and 1 tails. We can simply list these out:
HHHHT
HHHTH
HHTHH
HTHHH
THHHH
The only question is what day of the week the “down” day falls on, so there are 5 possibilities for a $3 increase. Alternatively, we can use the combinations or anagrams method to calculate (5!)/(4!) = 5.
Now, we need to count all the possible 5-day sequences of flips. Since each day can have 2 outcomes (H or T), we have 2 × 2 × 2 × 2 × 2 = 32 total possible outcomes over 5 days.
Finally, to compute the probability of a $3 increase over 5 days, we divide 5 successful outcomes by 32 total possibilities (of equal weight) to get 5/32.
The correct answer is (C).