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.

Question

Mathematics

Lennon Chen

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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Answers (1)

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Scarlet Gregory · Answer 1

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]