Q2 of 108 Page 271

Refer to Exercise 1 above. If the die were fair, determine whether or not the events A and B are independent

Given-


A= {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}


So, n(A)= 6, n(S)= (6)2= 36


∴


And B = {(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)}


n(B)= 6


∴


AՈB = [(5,5), (6,6)]


∴



Thus,


P (A Ո B) ≠ P(A). P(B)


So, A and B are not independent events.


More from this chapter

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1

For a loaded die, the probabilities of outcomes are given as under:

P (1) = P (2) = 0.2, P (3) = P (5) = P (6) = 0.1 and P (4) = 0.3.


The die is thrown two times. Let A and B be the events, same number each time and a total score is 10 or more respectively. Determine whether or not A and B are independent.

 3

The probability that at least one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate .

 4

A bag contains 5 red marbles and 3 black marbles. Three marbles are drawn one by one without replacement. What is the probability that at least one of the three marbles drawn be black, if the first marble is red?

 5

Two dice are thrown together and the total score is noted. The events E, F and G are ‘a total of 4’, ‘a total of 9 or more’, and ‘a total divisible by 5’, respectively. Calculate P(E), P(F) and P(G) and decide which pairs of events, if any, are independent.