The probability of any event is the sum of the probabilities pi of the
values of X that make up the event.
A bottle cap is tossed three times. We define the random variable X as the
number of number of times the cap drops with the open side up.
What is the probability that at least two
Value of X
0
1
2
3
times the cap lands with the open side
Probability
.027
.189
.441
.343
UDD
DUD
DDU
UUD
UDU
UUD
UUU
up ( at least two means two or
more )?
P(X ≥ 2) = P(X=2) + P(X=3) = .441 + .343 = 0.784
DDD
What is the probability that cap lands with the open side up fewer than three
times?
P(X<3) = P(X=0) + P(X=1) + P(X=2) = .027 + .189 + .441 = 0.657 or
P(X<3) = 1 – P(X=3) = 1 - 0.343 = 0.657