P(X< 3 n=15, successes=.4)
Think of a string of letters 15 places long.
“FFFFFFFFFFFFFFF” that would be a string of 15 failures and can happen in only with probability . That is because P(success) while P(failure) .
“SFFFFFFFFFFFFFF” that would be a string of 14 failures and one success. It can happen in 15 ways (S can be in 15 places). .
“SSFFFFFFFFFFFFF” that would be a string of 13 failures and two successes. It can happen in combination of 15 taken 2 at a time ways.