Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each
dice is:
Probability Even Numbers Dice Calculation
The question asks for the probability of rolling an even number on each of two identical dice rolled simultaneously.
Understanding Dice Outcomes
Each standard die has 6 faces, numbered 1 to 6. The total possible outcomes for a single die roll are {1, 2, 3, 4, 5, 6}.
- Total possible outcomes for one die: 6
Identifying Favorable Outcomes
We are interested in rolling an even number. The even numbers on a die are {2, 4, 6}.
- Number of even outcomes for one die: 3
Calculating Single Die Probability
The probability of rolling an even number on a single die is the ratio of favorable outcomes to total outcomes.
- $P(\text{Even on one die}) = \frac{\text{Number of even outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}$
Probability for Two Dice
Since the two dice are rolled simultaneously, the events are independent. The probability of independent events occurring together is the product of their individual probabilities. We need an even number on the first die AND an even number on the second die.
- $P(\text{Even on Die 1} \text{ and } \text{Even on Die 2}) = P(\text{Even on Die 1}) \times P(\text{Even on Die 2})$
- $P(\text{Both Even}) = \frac{1}{2} \times \frac{1}{2}$
- $P(\text{Both Even}) = \frac{1}{4}$
Conclusion
The probability that an even number is rolled on each die is $\frac{1}{4}$.
Important Questions from Probability
Two dice are thrown simultaneously and the sum of the numbers appearing on them is noted. What is the probability that the sum is 12?
If a box contains 3 white cushions, 4 red cushions and 5 blue cushions, what is the probability of selecting a white or blue cushion?
A. 2/3
B. 3/4
C. 1/4
D. 1/9Statements followed by some conclusions are given below.
Statements:
1. A bag has 2 white, 3 black, 4 red and 6 green balls.
2. 1 ball selected at random from the bag.
Conclusions:
I. The probability that a black ball is selected is 1/5
II. The probability that a red ball is selected is 6/15
Find which of the conclusions logically follows from the given statement
A. Only conclusion I follows.
B. Only conclusion II follows.
C. Both I and II follow.
D. Neither I nor II follows.
In a shooting test, the probabilities of hitting the target are 1/2 for A, 2/3 for B and 3/4 for C. If they fire at the same target, what is the probability that only one of them hits the target?
A bag contains balls numbered from 1 to 42. One ball is drawn at random from these balls. The probability that its number is a multiple of 7 or 8 is:
