Question

A box contains 46 red marbles, 59 white marbles, and 49 blue marbles. If a marble is randomly selected from the box, what is the probability that it is red or blue? Express your answer as a simplified fraction or a decimal rounded to four decimal places

Answer 1

Answer:

The probability of select randomly a red or a blue marble is $P(red \:or \:blue)=\frac{95}{154} \approx 0.6169$

Step-by-step explanation:

The probability of an event is the ratio of the number of ways it can happen, to the total number of possible cases.

Select randomly a red or a blue marble are mutually exclusive events because they cannot occur at the same time. When two events, A and B, are mutually exclusive, the probability that A or B will occur is the sum of the probability of each event.

$P(red \:or \:blue)= P(red) + P(blue)$

We know from the information given that

• There are 46 red marbles, 59 white marbles and 49 blue marbles

We can use this information to calculate the probability of select randomly a red marble and also the probability to select randomly a blue marble

$P(red)=\frac{46}{46+59+49}= \frac{23}{77}$

$P(blue)=\frac{49}{46+59+49}= \frac{7}{22}$

Now we can calculate the probability that we select a red or a blue marble

$P(red \:or \:blue)= P(red) + P(blue)\\P(red \:or \:blue)=\frac{23}{77} +\frac{7}{22} \\P(red \:or \:blue)=\frac{46}{154} +\frac{49}{154}\\P(red \:or \:blue)=\frac{95}{154} \approx 0.6169$