Two dice are tossed simultaneously. What is the probability that “either the sum of top faces of dice is six
or both top faces are similar”?
sum of six:
1,5 2,4 3,3 4,2 5,1 ---> 5 ways
top faces the same:
1,1 2,2 3,3 4,4 5,5 6,6 ---> 6 ways
number of ways of our event = 5+6-1 (can't count the 3,3 twice)
= 10
prob(of our event) = 10/36 = 5/18
To find the probability in this case, we need to determine the total number of favorable outcomes and the total number of possible outcomes.
Let's break it down step by step:
Step 1: Calculate the total number of possible outcomes.
When two dice are tossed simultaneously, the total number of outcomes is given by the product of the number of outcomes for each die. Since each die has six faces, the number of possible outcomes is 6 multiplied by 6, which equals 36.
Step 2: Calculate the number of favorable outcomes.
A) Favorable outcome: The sum of the top faces of the dice is six.
To determine the number of favorable outcomes in this case, we need to find all the combinations of two numbers that add up to six. These combinations are:
(1,5), (2,4), (3,3), (4,2), and (5,1). So, there are five favorable outcomes.
B) Favorable outcome: Both top faces are similar.
There are six possible outcomes in this case, as each number from 1 to 6 can appear on both dice.
The total number of favorable outcomes is 5 + 6 = 11.
Step 3: Calculate the probability.
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes.
So, the probability is: 11/36.
Thus, the probability that either the sum of the top faces of the dice is six or both top faces are similar is 11/36.