Question

An entrance exam is based on two papers A and B. The probability of passing
one paper A by a randomly selected student is 80% and passing paper B is
70%. The passing at least A or B is 95%. Find the probability that the student
passes both the
papers.​

Answer 1

Step-by-step explanation:

Let A and B denotes the events that a randomly chosen student passes first and second examinations respectively. 

Then, P(A)=0.8 

P(B)=0.7 

P(A∪B)=0.95

Required probability =P(A∩B) 

P(A)+P(B)−(A∪B) 

⇒0.8+0.7−0.95=0.55

#aswad

Answer 2

Answer:

Here we will go to find the probability that the student passes both the papers using the given data.

Answer: The probability that the student passes both the papers $=55\%$

Step-by-step explanation:

From the given question,

• An entrance exam is based on two papers A and B.
• The probability of passing one paper A by a randomly selected student is 80%.It should be written as,

                  $P(A)=80\%$

• The probability of passing another paper B by a randomly selected student is 70%.It should be written as,

                  $P(B)=70\%$

• The probability of passing at least one paper A or B is 95%.That is,

            $P(A\cup B)=95\%$

• Using the above information we can find the probability that the student passes both the papers. That is $P(A\cap B)=?$
• Already we know the formula for $P(A\cap B)$  

             $P(A\cap B)=P(A)+P(B)-P(A\cup B)$

                             $=80\%+70\%-95\%$

                             $=150\%-95\%$

             $P(A\cap B)=55\%$

Final Answer:

The probability that the student passes both the papers $=55\%$