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23 June, 22:06

Coin which lands heads with probability p is tossed repeatedly. assuming independence of the tosses, find formulae for

a. the probability that exactly 5 heads appear in the first 9 tosses;

b. the probability that the first head appears on the 7th toss;

c. the probability that the fifth head appears on the 12th toss;

d. the probability that the same number of heads appear in the first 8 tosses as in the next 5 tosses;

e. the probability that the 10th toss is either the 4th or 5th head.

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  1. 23 June, 23:00
    0
    A. (9 5) (p^5) [ (1-p) ^4]

    b. p[ (1-p) ^6]

    c. (11 4) (p^5) [ (1-p) ^7]

    d. (1-p) ^13 + (8 1) (5 1) (p^2) [ (1-p) ^11] + (8 2) (5 2) (p^4) [ (1-p) ^9] + (8 3) (5 3) (p^6) [ (1-p) ^7] + (8 4) (5 4) (p^8) [ (1-p) ^5] + (8 5) (p^10) [ (1-p) ^3]

    e. (9 3) (p^4) [ (1-p) ^6] + (9 4) (p^5) [ (1-p) ^5]
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