Probability

Total numbers
Numbers divisible by

Number divisible by

Total number of numbers divisible by 6 or 8

Required probability

Total number of cases
Favourable cases are

Total number of favourable cases
Required probability

Given,
and

Given, and

..(i)



From E (i),

Since, each person can leave the cabin at any floor. Total number of ways,
Required probability

p = P (success) = P (getting number greater than 4)




By Binomial distribution P (probability of atleast 2 successes)

Given, We know that, if
then and
Here, we have


and


Hence,

In the given binomial distribution, ,

Mean

( speaks truth)
( speaks truth)

and
Required probability



Thus, in cases they are likely to contradict each other in stating the same fact

Step 1: Use the Formula for the Union of Events
We know that: We are given: From the formula, we can solve for .
Step 2: Determine Dependence
If and were independent, we would have: However, from the given data, does not equal , implying that and are dependent.
Step 3: Conclusion
Thus, the correct answer is that A and B are dependent events.

Since and are mutually exclusive, the probability that neither event occurs is the complement of the probability that at least one of the events occurs.
This can be expressed as: Since and are mutually exclusive, we know: Therefore: Conclusion Thus, the correct answer is .

Step 1: Total Probability for Black Balls
The total number of balls is .
The probability of drawing a black ball on a single trial is: The probability of not drawing a black ball is:
Step 2: Calculate the Probability of At Least Two Black Balls
The probability of drawing 0 or 1 black ball in 4 trials is easier to compute first, and we subtract it from 1 to get the probability of drawing at least 2 black balls. Probability of 0 black balls: Probability of 1 black ball:
Step 3: Final Calculation
Thus, the probability of drawing at least two black balls is:
Step 4: Conclusion
Thus, the correct answer is .