Answer :
Answer:
A) 1/n²
B) (n - 1)/n²
C) Probability = (1 - (1/n))/2
Step-by-step explanation:
A) We are told that a ticket is drawn at random from the box. Thereafter, the ticket is replaced in the box and a second ticket is now drawn at random.
This means the events of the first and second tickets are independent.
Probability of first ticket = 1/n
Probability of 2nd ticket = 1/n
Probability of both together = 1/n × 1/n = 1/n²
B) The number on the 2 tickets are consecutive integers.
This means number of cases will be (n - 1)
From a above, we see that for the two tickets the denominator is n²
Thus, in this case, the probability that both that the numbers on the two tickets are consecutive integers = (n - 1)/n²
C) if we assume that the first ticket is b, then the number of correct selections for the 2nd ticket is (n - b).
Thus, number of correct selections is;
(n_Σ_k=1) (n - b) = n² - (n(n - 1)/2)
Simplifying this gives;
(2n² - n² - n)/2
>> ½(n² - n)
There are n² selections in total, thus let's factorize n² out and then the remaining part in bracket will be the probability. Thus;
>> n²(1 - (1/n))/2
Probability = (1 - (1/n))/2