A box contains four red marbles, seven white marbles and five blue marbles. If one marble is drawn at random, find the probability for each of the following:
(a) A blue marble drawn. _____________
(b) A red or a blue marble is drawn. _____________
(c) Neither a red nor a blue marble is drawn. _____________
a 5/16
b 9/16
c 7/16
I believe you're right
To find the probability for each scenario, we need to calculate the ratio between the favorable outcomes and the total number of possible outcomes.
Total number of marbles in the box = 4(red) + 7(white) + 5(blue) = 16 marbles
(a) Probability of drawing a blue marble:
Number of favorable outcomes (blue marbles) = 5
Total number of possible outcomes (total marbles) = 16
Probability = favorable outcomes / total outcomes = 5/16
(b) Probability of drawing a red or a blue marble:
Number of favorable outcomes (red + blue marbles) = 4(red) + 5(blue) = 9
Total number of possible outcomes (total marbles) = 16
Probability = favorable outcomes / total outcomes = 9/16
(c) Probability of neither a red nor a blue marble is drawn:
Number of favorable outcomes (white marbles) = 7
Total number of possible outcomes (total marbles) = 16
Probability = favorable outcomes / total outcomes = 7/16
Therefore, the probabilities are:
(a) Probability of drawing a blue marble = 5/16
(b) Probability of drawing a red or a blue marble = 9/16
(c) Probability of neither a red nor a blue marble is drawn = 7/16