In: Statistics and Probability
A hat contains a number of cubes: 3 red, 2 white, 1 blue, and 4 black.
Total cubes = 10
a) P(red cube) = n(red cube) /10 = 3/10 = 0.3
Therefore 0.3 is the required probability here.
b) P(not a red cube) = 1 - P(red cube) = 1 - 0.3 = 0.7
Therefore 0.7 is the required probability here.
c) P(white or black) = P(white) + P(black) = 0.2 + 0.4 = 0.6
Therefore 0.6 is the required probability here.
d) P(neither black nor white) = 1 - P(white or black) = 1 - 0.6 = 0.4
Therefore 0.4 is the required probability here.
e) Sum of the probabilities in a and b are computed here as:
P(red cube) + P(not a red cube) = 0.3 + 0.7 = 1
As the we are adding complement events here, therefore the sum of probabilities here is 1.
f) As the cubes are taken out with replacement, the probability that all are white is computed here as:
= [P(white)]3
= 0.23 = 0.008
Therefore 0.008 is the required probability here.
g) P(none are white) = 0.83 = 0.512
Therefore 0.512 is the required probability here.
h) Probability that at least one of them is white
= 1 - Probability that none are white
= 1 - 0.512
= 0.488
Therefore 0.488 is the required probability here.