Question

An integer is chosen at random and squared. The probability that the last digit of the square is 1 or 5 is
a) \[\dfrac{2}{{10}}\]
b) \[\dfrac{3}{{10}}\]
c) \[\dfrac{4}{{10}}\]
d) \[\dfrac{9}{{10}}\]

Answer 1

Hint: Here the question is related to the probability. On reading the question first we write the sample space of the problem and the number of elements present in the sample space. Based on the question, we write the event and the number of elements in the event. Then on using the formula \[P(E) = \dfrac{{n(E)}}{{n(S)}}\], where E is the event.

Complete step-by-step answer:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are to happen, using it. Probability can range in from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
The probability formula is defined as the probability of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
\[Probability\; of\; event \;to \;happen \;P\left( E \right) = \dfrac{{Number \;of \;favourable \;outcomes}}{{Total \;Number \;of \;outcomes}}\]
Consider the given question:
The sample space contains \[S = \{ 0,1,2,3,4,5,6,7,8,9\} \]. Therefore the number of elements in the sample space is \[n(S) = 10\].
Let A be the event where the number is squared the last digit will be 1 or 5. The elements in the event A will be \[A = \{ 1,5,9\} \]. Therefore the number of elements in the event A is \[n(A) = 3\]
Now we have
\[ \Rightarrow P(A) = \dfrac{{n(A)}}{{n(S)}}\]
On substituting the values we get
 \[ \Rightarrow P(A) = \dfrac{3}{{10}}\]
Hence option b) is the correct one.
So, the correct answer is “Option b”.

Note: The probability is a number of possible values, students must know the definition and the basic theorem of probability like addition and multiplication theorem. The word ‘or’ will represents the union of two events ‘and’ the word and represents the intersection of two events. If there is no common term in the both events it means it is called independent events.