GRE STATISTICS, PERMUTATIONS AND COMBINATIONS, PROBABILITY
- 2. For a frequency distribution , mean = 𝑓𝑥 𝑓 mathews.suman@gmail.com
- 3. Find the mean and median of the random variable X, from the table below X RELATIVE FREQUENCY 0 0.18 1 0.33 2 0.10 3 0.06 4 0.33 cf 0.18 0.51 0.61 0.67 1 1 2 = .5 Median = 1 fx 0 0.33 0.2 0.18 1.32 2.03 Mean = 2.03/1=2.03 mathews.suman@gmail.com
- 4. Number of arrangements of n objects= n!= n(n-1)(n-2)---------1 Fundamental principle of counting If a certain event can occur in m different ways, another event can occur in n different ways, then both the events together can occur in 𝑚 × 𝑛 different ways. mathews.suman@gmail.com
- 5. A invites 4 friends to go to the movies. There are a row of 5 seats, one person per seat. In how many ways can they be seated with A sitting in the middle seat. _____. _____. _A___. ____. _______ A can be seated in the middle in exactly 1 way. There are 4 seats left. The 4 persons can be seated in 4! ways. Ans = 16 mathews.suman@gmail.com
- 6. How many 3 digit positive numbers are odd and do not contain the digit 5 The digit’s place can be 1,3,7 or 9. This can be filled in 4 ways ___. ____. ____ The 100th place cannot be 0 or 5, Hence it can be filled in 8 ways. The 10th place cannot be 5. So it can be filled in 9 ways. Ans = 8 × 9 × 4 = 288 mathews.suman@gmail.com
- 7. Probability of at least one = 1- P(none) mathews.suman@gmail.com
- 8. A marble is selected at random 3 times from a bag of 2 green, 2 blue and 2 red marbles. The selected marble Is replaced each time. What is the probability that at least one of the marbles is blue. P(at least one is blue) = 1 – P(none are blue) = 1 − 2 3 2 3 ( 2 3 ) = 1 − 8 27 = 19 27 mathews.suman@gmail.com