Question

Mark for review Question: 8 The probability of students appeared for CAT is 4/5 and for MAT is 2/5. Then find out the probability that student appeared for at least one test​

Answer 1

Step-by-step explanation:

let us consider,

probability of students appeared for CAT

is P(A)= 4/5

probability of students appeared for MAT

is P(B)=2/5

probability that student appeared for atleast

one test is = P(A)+P(B)-P(A)*P(B)

Answer is 22/25

Answer 2

PROBABILITY IS 22/25.

Given:

The probability of students appeared for CAT is 4/5 and for MAT is 2/5.

To find:

Find out the probability that student appeared for at least one test.

Solution:

We have to find the probability of students not appearing for CAT and MAT and then we have to multiply making a case if only students appear for CAT and not MAT and then if students appear for only MAT and not CAT and if students appear for both and then we have to add all the three cases.

If the probability of ​students appearing for CAT IS 4/5, Then probability of students not appearing for CAT is 1 - 4/5 = (5-4)/5 = 1/5

Similarly,

If the probability of ​students appearing for MAT IS 2/5, Then probability of students not appearing for MAT is 1 - 2/5 = (5-2)/5 = 3/5

To find out out the probability of at least one student appearing for either test, we have to find out in three situations.

First one is when students appeared for CAT and not for MAT

Probability of students appearing for CAT and not MAT = P(CAT) * P(not MAT) = 4/5 * 3/5 = 12/25

Second one is when students appeared for MAT and not for CAT

Probability of students appearing for MAT and not CAT = P(MAT) * P(not CAT) = 2/5 * 1/5 = 2/25

Now third is when both appeared for test

Probability of both appearing for test = P(CAT) * P(MAT)

= 4/5*2/5 = 8/25

Now, we will add all three to get the probability of at least one test appearance

P(at least one) = 12/25 + 2/25 + 8/25 = 22/25

Hence, probability that student appeared for at least one test​ is 22/25.

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