A loaded die has the property that the probability of throwing an odd number is three time the probability of throwing an even number. If the even number are equally
likely to appear, find the probability of rolling either a 3 or a 6.
P(odd)=0.75
P(even)=0.25
P(3)=0.75/3=1/4
P(6)=0.25/3=1/12
Since 3 and 6 are mutually exclusive,
P(3∪6)=P(3)+P(6)=1/4 + 1/12 = 1/3
To solve this problem, we need to set up equations based on the given information.
Let's assume that the probability of rolling an odd number is "p".
Since the probability of rolling an even number is equally likely, the probability of rolling an even number is 1 - p.
According to the problem, the probability of rolling an odd number is three times the probability of rolling an even number. So, we can set up the equation:
p = 3 * (1 - p)
Now, let's solve for p:
p = 3 - 3p
4p = 3
p = 3/4
Therefore, the probability of rolling an odd number is 3/4, and the probability of rolling an even number is 1 - 3/4 = 1/4.
To find the probability of rolling either a 3 or a 6, we need to find the probabilities of rolling each number and then add them together.
The probability of rolling a 3 is the probability of rolling an odd number, which is 3/4.
The probability of rolling a 6 is the probability of rolling an even number, which is 1/4.
Therefore, the probability of rolling either a 3 or a 6 is 3/4 + 1/4 = 4/4 = 1.