1. A coin has P(T) = 2/5. If it is tossed five times in succession, find the pro

Question

1. A coin has P(T) = 2/5. If it is tossed five times in succession, find the probability of getting
           a. Exactly two head;
           b. At most one head;
           c. At least one head;
2. A fair die is tossed twice. Let A be the event the total is at least eight, B the event the total is at most nine, and C the event the total is odd. Find
           a. P( A | B );
           b. P( B | A );
           c. P( A | C );
           d. P( C | A );
           e. P( B | C );
           f. P( C | B );
3.
           a. Find the probability that everyone in a group of n <= 365 people has a different birthday. (Ignore birthdays on February 29 and assume that all 365 days of the year are equally likely birthdays.)
           b. Find the value of n such that the probability in (a) is as close as possible to .

4. A new three-screen cinema has just opened in the town of Quirpoon. The table summarizes the fraction of customers attending each of the three movies showing on a given night and, for each film, the fraction who purchase popcorn.

Find the probability that
           a. A randomly selected patron attends La Vie dum Elan and purchases popcorn;
           b. A randomly selected patron attends Rarer Birds and does not purchase popcorn;
           c. A randomly selected patron purchases popcorn;
           d. A customer attending Rarer Birds or Codroy Vampire Project does not purchase popcorn;
           e. A customer who attends La Vie dun Elan purchases popcorn

1. A coin has P(T) = 2/5. If it is tossed five times in succession, find the probability of getting a. Exactly two head; b. At most one head; c. At least one head; 2. A fair die is tossed twice. Let A be the event the total is at least eight, B the event the total is at most nine, and C the event the total is odd. Find a. P( A | B ); b. P( B | A ); c. P( A | C ); d. P( C | A ); e. P( B | C ); f. P( C | B ); 3. a. Find the probability that everyone in a group of n

Explanation / Answer

1) P(T) = 2/5, P(H) = 1 - 2/5 = 3/5

a) exactly two head

using binomial expansion

5C2 * (3/5)^2 * (2/5)^3 = 10 * (0.36) * (0.064) = 0.36 * 0.64 = 0.2304

b) atmost one head

using binomial expansion

5C0 * (3/5)^5 * (2/5)^0 + 5C1 * (3/5)^4 * (2/5)^1 = 0.33696

c) atleast one head

P(atleast one head) = 1 - P(no head) = 1 - (0.6)^5 = 0.9224

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