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Introduction to Probability. Natalia Sivackova. Equally Likely Events. Coin toss example: Probability of result is ½ Dice example: Probability of result is 1/6 For nth term Probability = 1/n. Not Equally Likely Events. Bag of marbles 4 blue 5 green 6 red Probability of picking blue?
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Introduction to Probability Natalia Sivackova
Equally Likely Events • Coin toss example: • Probability of result is ½ • Dice example: • Probability of result is 1/6 • For nth term • Probability = 1/n
Not Equally Likely Events • Bag of marbles • 4 blue • 5 green • 6 red • Probability of picking blue? • 4/15
General Formula • The bag is U • n(U) = 15 • Blue marbles form a subset A U • Probability of picking a member of A is P(A) • P(A) = n(A)/n(U)
Probability of a Complementary Event • Sock drawer contains 53 socks • 13 are single socks • 40 are in a pair • Probability of single sock: n(S)/n(U) = 13/53 • Probability of a sock from a pair: n(S’)/n(U) = 40/53 • P(S) + P(S’) = 53/53 = 1 • Generalized formula for all subsets: P(S’) = 1 – P(S) • S S’ = U
Cont. • When an event is certain it has a probability of 1 • When an event is impossible it has a probability of 0 (e.g. of an impossible event) S S’ = (You cannot pick a sock that is both single and part of a pair)
