Let's break down each of the parts and explain the probabilities step by step.
### (a) On throwing a dice, the probability of getting an even number is __________
When you throw a six-sided dice, there are 6 possible outcomes: 1, 2, 3, 4, 5, 6. Out of these, the numbers that are even are 2, 4, and 6. Hence, there are 3 favorable outcomes out of 6 possible outcomes. The probability of an event can be found by dividing the number of favorable outcomes by the total number of possible outcomes.
So, the probability [tex]\( P(\text{even number}) \)[/tex] is:
[tex]\[ P(\text{even number}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} = \frac{3}{6} = 0.5 \][/tex]
### (b) The probability of the Sun rising from the west on a particular day is __________
The Sun rises from the east every day; it never rises from the west. Thus, the event of the Sun rising from the west is impossible. In probability, an impossible event has a probability of 0.
So, the probability [tex]\( P(\text{Sun rising from the west}) \)[/tex] is:
[tex]\[ P(\text{Sun rising from the west}) = 0 \][/tex]
### (c) The probability of getting either heads or tails on tossing a coin is __________
When you toss a fair coin, there are 2 possible outcomes: heads or tails. Both are equally likely. Since the question asks for the probability of getting either heads or tails, both outcomes are favorable.
So, the probability [tex]\( P(\text{heads or tails}) \)[/tex] is:
[tex]\[ P(\text{heads or tails}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} = \frac{2}{2} = 1.0 \][/tex]
### Summary
- (a) The probability of getting an even number when throwing a dice is [tex]\( 0.5 \)[/tex].
- (b) The probability of the Sun rising from the west on a particular day is [tex]\( 0 \)[/tex].
- (c) The probability of getting either heads or tails on tossing a coin is [tex]\( 1.0 \)[/tex].
