ProbabilityHard
Question
A bag contains four tickets marked with numbers 112, 121, 211, 222. One ticket is drawn at random from the bag. Let Ei(i = 1, 2, 3) denote the event that ith digit on the ticket is 2. Then
Options
A.E1 and E2 are independent
B.E2 and E3 are independent
C.E3 and E1 are independent
D.E1, E2, E3 are independent
Solution
E1 → p first digit is ′2′ ⇒ 211 or 222
P(E1) =
E2 → second digit is ′2′ ⇒ 121, 222
P (E2) =
E3 third digit is ′2′ ⇒ 222 & 112
P(E3) =
(E1 ∩ E2) = 222 ⇒ P(E1 ∩ E2) =
= P (E1) P (E2)
Similiarly E2 & E3, E1 & E3
also E1 ∩ E2 ∩ E3 → 222 ⇒ P(E1 ⎳ E2 ∩ E3) =
P(E1) P(E2) P(E3)
P(E1) =
E2 → second digit is ′2′ ⇒ 121, 222
P (E2) =
E3 third digit is ′2′ ⇒ 222 & 112
P(E3) =
(E1 ∩ E2) = 222 ⇒ P(E1 ∩ E2) =
= P (E1) P (E2)Similiarly E2 & E3, E1 & E3
also E1 ∩ E2 ∩ E3 → 222 ⇒ P(E1 ⎳ E2 ∩ E3) =
P(E1) P(E2) P(E3)Create a free account to view solution
View Solution FreeMore Probability Questions
Three cards are drawn from a pack of 52 cards. The probability that they are of the same colour is-...A bag contains 7 tickets marked with the numbers 0, 1, 2, 3, 4, 5, 6 respectively. A ticket is drawn & replaced. Then th...A & B throw with one dice for a stake of Rs. 99/- which is to be won by the player who first throws 4. If A has the firs...There are 4 urns. The first urn contains 1 white & 1 black ball, the second urn contains 2 white & 3 black balls, the th...A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is a...