onany given day the probability that the share price of a co

onany given day, the probability that the share price of a company\'s stock will rise is 0.6. Assume that day-to-day share price movements are independent. What\'s the probability that the share price:

(a) Will rise for 4 consecutive days?

(b) Rises for the first time on the third day of the week?

(c) Falls for 5 consecutive days?

(d) Falls on at least one day of the week?

(e) Rises on the first two days and falls during the rest of the week?

Solution

a)

P(rise 4 consecutive) = 0.6*0.6*0.6*0.6 = 0.1296

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b)

P(fall, fall, rise) = 0.4*0.4*0.6 = 0.096

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c)

P(fall 5 consecutive) = 0.4*0.4*0.4*0.4*0.4 = 0.01024

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d)

P(fall at least one day) = 1 - P(rise 7 days)

= 1 - 0.6^7

= 0.9720064

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e)

P(rise, rise, fall, fall,fall,fall,fall) = 0.4*0.4*0.6*0.6*0.6*0.6*0.6

= 0.0124416 [ANSWER]