5. You have two normal six-sided dice. In one roll of the two dice, what is the probability that both sides show the same number? A. 1/36 B. 6/36 C. 12/36 D. 36/36 6. The statistics of the maximum temperature in a given area for the month of June show that it was above 20°C twenty one times in the past 100 years and below 13°C in 18 of the last 100 years. Calculate the probability that the maximum temperature during the last 100 years was between 13 and 20°C. A. 0.29 B. 0.39 C. 0.61 D. 0.79

Let's tackle each part of the question one by one:

Probability that both dice show the same number:


In a single roll of two six-sided dice, each die has 6 faces, numbered from 1 to 6.
To find the probability that both dice show the same number, we need to consider the different outcomes where this happens. These outcomes are pairs like (1,1), (2,2), ..., (6,6).
There are 6 such pairs: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6).
The total number of possible outcomes when rolling two dice is 6 * 6 = 36.
So, the probability that both dice show the same number is the number of successful outcomes (same number on both dice) divided by the total number of outcomes: 36 6 ​ = 6 1 ​ .

Therefore, the correct choice is B. 6/36 .

Probability that the maximum temperature was between 13°C and 20°C during the last 100 years:


According to the given statistics:

The maximum temperature was above 20°C twenty-one times.
The maximum temperature was below 13°C eighteen times in the last 100 years.


To find the probability that the temperature was between 13°C and 20°C, we count the number of years it was within this range.

First, calculate the number of years where the temperature was outside the range:

Above 20°C: 21 times
Below 13°C: 18 times


The total number of times the temperature was outside the 13°C to 20°C range is 18 + 21 = 39.

Therefore, the number of years it was between 13°C and 20°C is 100 - 39 = 61.

So, the probability is the number of times within the range divided by the total years: 100 61 ​ = 0.61 .


Therefore, the correct choice is C. 0.61 .

Answered by SophiaElizab | 2025-07-21