j_shreyans wrote:Every trading day, the price of CF Corp stock either goes up by $1 or goes down by $1 with equal likelihood. At the end of 5 trading days, what is the probability that the price of CF Corp stock is up by exactly $3 from its initial price?

A)1/16
B)1/8
C)5/32
D)9/32
E)3/8

To be $3 higher at the end of 5 trading days, the price must go UP by $1 on exactly 4 days and go DOWN by $1 on exactly 1 day.
Question stem, rephrased:
What is the probability that the stock goes down on EXACTLY ONE day?

P(exactly N times) = P(one way) * (all possible ways)

Let U = up and D = down.
Since the stock goes up or down with EQUAL LIKELIHOOD, P(U) = 1/2 and P(D) = 1/2.

ONE WAY:
One way to get a favorable outcome is UUUUD, implying that the stock goes up on the first 4 days and down on the last day.
P(UUUUD) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32.

ALL POSSIBLE WAYS:
Since D could happen on any of the 5 days -- a favorable outcome will be achieved by UUUUD, UUUDU, UUDUU, UDUUU, or DUUUU, for a total of 5 ways -- we multiply by 5:
5 * (1/32) = 5/32.

The correct answer is C.

j_shreyans wrote:Every trading day, the price of CF Corp stock either goes up by $1 or goes down by $1 with equal likelihood. At the end of 5 trading days, what is the probability that the price of CF Corp stock is up by exactly $3 from its initial price?

A)1/16
B)1/8
C)5/32
D)9/32
E)3/8



OAC

For $3 up the price must go up on 4 days and doen on 1 day

therefore favorable cases = 5C4 = 5

Total Outcomes = 2x2x2x2x2 = 32

Probability = 5/32

Answer: Option C