Answer
Verified
378.6k+ views
Hint: We first assume the events for the given probabilities. We use the formula of \[p\left( A\cup B \right)=p\left( A \right)+p\left( B \right)-p\left( A\cap B \right)\]. Then we use events A and B are independent and therefore we can write $p\left( A\cap B \right)=p\left( A \right)p\left( B \right)$.
Complete step by step answer:
The probability of getting a girl student selected for IAS is $0.4$ and that of a boy candidate selected is $0.6$. We assume them as events where we take event A for probability of getting a girl student selected for IAS and event B for probability of getting a boy student selected for IAS.So,
$p\left( A \right)=0.4$ and $p\left( B \right)=0.6$
The probability that at least one of them will be selected for IAS can be expressed as $p\left( A\cup B \right)$. The events A and B are independent and therefore we can write,
$p\left( A\cap B \right)=p\left( A \right)p\left( B \right)$
We also can express,
\[p\left( A\cup B \right)=p\left( A \right)+p\left( B \right)-p\left( A\cap B \right)\]
Putting the values, we get
\[p\left( A\cup B \right)=p\left( A \right)+p\left( B \right)-p\left( A\cap B \right) \\
\Rightarrow p\left( A\cup B \right)=0.4+0.6-0.4\times 0.6 \\
\therefore p\left( A\cup B \right)=0.76\]
Hence, the correct option is A.
Note:We use the independent event to find the dependency for the given probabilities. In case of exclusiveness, we could have written it in the form of $p\left( A\cap B \right)=0$.Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.
Complete step by step answer:
The probability of getting a girl student selected for IAS is $0.4$ and that of a boy candidate selected is $0.6$. We assume them as events where we take event A for probability of getting a girl student selected for IAS and event B for probability of getting a boy student selected for IAS.So,
$p\left( A \right)=0.4$ and $p\left( B \right)=0.6$
The probability that at least one of them will be selected for IAS can be expressed as $p\left( A\cup B \right)$. The events A and B are independent and therefore we can write,
$p\left( A\cap B \right)=p\left( A \right)p\left( B \right)$
We also can express,
\[p\left( A\cup B \right)=p\left( A \right)+p\left( B \right)-p\left( A\cap B \right)\]
Putting the values, we get
\[p\left( A\cup B \right)=p\left( A \right)+p\left( B \right)-p\left( A\cap B \right) \\
\Rightarrow p\left( A\cup B \right)=0.4+0.6-0.4\times 0.6 \\
\therefore p\left( A\cup B \right)=0.76\]
Hence, the correct option is A.
Note:We use the independent event to find the dependency for the given probabilities. In case of exclusiveness, we could have written it in the form of $p\left( A\cap B \right)=0$.Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE