S = 52 cards
⇒ 52 Two cards are drawn without replacement.
A = {26 black cards}
⇒ n(A) = 26
P(A) = \(\frac {26}{52}\)
And P(B) i.e., the probability that the second card is black known that the first card is black = \(\frac {25}{51}\)
P(A and B) = P(A).P(B)
= \(\frac {26}{52} ×\frac {25}{51}\)
= \(\frac {1}{2} ×\frac {25}{51}\)
= \(\frac {25}{102}\)
A shop selling electronic items sells smartphones of only three reputed companies A, B, and C because chances of their manufacturing a defective smartphone are only 5%, 4%, and 2% respectively. In his inventory, he has 25% smartphones from company A, 35% smartphones from company B, and 40% smartphones from company C.
A person buys a smartphone from this shop
A shop selling electronic items sells smartphones of only three reputed companies A, B, and C because chances of their manufacturing a defective smartphone are only 5%, 4%, and 2% respectively. In his inventory, he has 25% smartphones from company A, 35% smartphones from company B, and 40% smartphones from company C.
A person buys a smartphone from this shop
(i) Find the probability that it was defective.
In accordance with the multiplication rule of probability, the probability of happening of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A happens given that event B occurs.
Let's assume, If A and B are dependent events, then the probability of both events occurring at the same time is given by:
\(P(A\cap B) = P(B).P(A|B)\)
Let's assume, If A and B are two independent events in an experiment, then the probability of both events occurring at the same time is given by:
\(P(A \cap B) = P(A).P(B)\)
Read More: Multiplication Theorem on Probability