Probability of Dependent and Independent Events

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Dependent and Independent Events in Probability • In this class, We discuss Dependent and Independent Events in Probability. • The reader should have prior knowledge of mutually exclusive events. Click Here. • Dependent Events: • Two events A and B, are said to be dependent if occurring of event A will affect the probability of event B. • Example: • A bag contains five black and six green balls. • Randomly pick a ball fom the bag two times. • A = First time, should pick a black ball • B = Second time, should pick a black ball • Probability to pick a black ball the first time = 5c1/11c1 • The probability of selecting a black ball a second time depends on the first-time selection. • First attempt if we select green ball. Probability of selecting black ball second time = 5c1/10c1 • First attempt if we select black ball. Probability of selecting black ball second time = 4c1/10c1 • Our conditional probability class discussed how to find the probability of dependent events? • After selecting a ball the first time in the above random experiment, we are not replacing the ball in the bag. • We are selecting with replacement. • Independent Events: • First time probability of picking black ball = 5c1/11c1 • Now we replace the ball in the bag. • Second-time probability to pick a black ball = 5c1/11c1 • Whatever ball we pick the first time, with replacement, the probability of a second attempt is not getting affected. • We call these types of events independent events. • Independent Events: • Two events, A and B, are said to be independent events. • The occurrence of one event will not affect the probability of another event. • Another Example: • Toss a coin two times. • A = First time should toss head. • B = Second time should toss head. • When we toss the first-time coin probability of getting a head = 1/2 • When we toss the coin a second time. probability of getting a head = 1/2 • The first event will not affect the probability of the second event. • Independent Events: • P(A ∩ B) = P(A) P(B) • P(A ∩ B) = occurring of both the events. • From the random experiment, toss a coin two times. P(A ∩ B) = 1/2 * 1/2 = 1/4 • Proof: • Toss the coin two times. • P(Both Heads)? • Sample Space S = {HH, HT, TH, TT} • Event E = {HH} • P(E) = 1/4. • • Link for playlists: • / @learningmonkey • • Link for our website: https://learningmonkey.in • Follow us on Facebook @ / learningmonkey • Follow us on Instagram @ / learningmonkey1 • Follow us on Twitter @ / _learningmonkey • Mail us @ [email protected]

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