Question

To play lotus in PR you must select 6 numbers between 1 and 42. On the day of the draw 6 numbers will be drawn at random, without replacement (between 1 and 42) of a tombola. If they are the same 6 numbers that you chose, you will win the jackpot.
a. How many different plays can you make? (How many combinations of 6 numbers are possible?) (5 pts)
b. What is the probability of winning the jackpot if you bought three different combinations? (5 pts)
c. What is the probability of hitting 5 of the 6 numbers on a particular move? (5 pts)

Answer 1

a) The number of ways to select 6 numbers from 42 numbers is computed here as:

b) The probability of winning the jackpot if we bought three different combinations is computed here as:
= 3 / Total number of combinations possible

= 3 / 5245786

= 0.000000571887607

Therefore 0.000000571887607 is the required probability here.

c) The probability of hitting 5 of the 6 numbers on a particular move is computed here as:

= Number of ways to select 5 numbers from the 6 numbers selected * Number of ways to select the 6th number from the remaining 36 numbers / Total ways to select 6 numbers from 42 numbers

Therefore 0.000041175907671 is the required probability here.