1.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 is drawn: ______
b.A red or blue marble is drawn: _____
c.Neither a blue or red marble is drawn:
a. (number of blue marbles)/(total number of marbles)
b. and c. Use similar logic for the other questions. Nine out of 16 are red OR blue.
4/5
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To find the probability for each of the given scenarios, we need to determine the total number of possible outcomes (denominator) and the number of favorable outcomes (numerator).
a) Probability of drawing a blue marble:
The total number of marbles in the box is 4 + 7 + 5 = 16.
There are 5 blue marbles in the box, so the probability of drawing a blue marble is:
P(blue marble) = Number of favorable outcomes / Total number of outcomes = 5/16.
b) Probability of drawing a red or blue marble:
The total number of marbles in the box is still 16.
The number of favorable outcomes is the sum of red and blue marbles, which is 4 + 5 = 9.
So, the probability of drawing a red or blue marble is:
P(red or blue marble) = Number of favorable outcomes / Total number of outcomes = 9/16.
c) Probability of neither a blue nor red marble being drawn:
In this case, we need to find the probability of drawing a white marble.
The total number of marbles in the box is 16, and there are 7 white marbles.
So, the probability of drawing a white marble is:
P(white marble) = Number of favorable outcomes / Total number of outcomes = 7/16.
To calculate the probability of neither a blue nor red marble being drawn, we subtract the probability of drawing a blue marble and the probability of drawing a red marble (found in a and c respectively) from 1, as only these three colors exist, we can conclude that:
P(neither blue nor red marble) = 1 - P(blue marble) - P(red marble).
Given that P(blue marble) = 5/16 and P(red marble) = 4/16:
P(neither blue nor red marble) = 1 - 5/16 - 4/16 = 7/16.