NIMCET 2014 Question Paper with solutions

Question : 3 of 120

Marks: +1, -0

A chain of video stores sells three different brands of DVD players. Of its DVD player sales 50% are brand 1, 30% are brand 2 and 20% are brand 3 Each manufacturer offers one year warranty on parts and labour. It is known that 25% of brand 1 DVD playersrequire warranty repair work, whereas the corresponding percentage for brands 2 and 3 are 20% and 10% respectively. The probability that a randomly selected purchaser has a DVD player that will need repair while under warranty, is

0.795
0.205
0.1250
0.060

Validate

Solution:

Let probability of sale of brand 1 is P(A).
Similarly, for brand 2 is P(B)
and brand 3 is P(C)
Given,
P (A) =

{50}/{100}

1/2

P (B) =

{30}/{100}

3/{10}

P (C) =

{20}/{100}

1/5

and also tet the probability of required warranty work of brand (1) is P (A)
Similarly, for brand 2 is P(B)
and for brand 3 is P(C).
∴ P (A) =

{25}/{100}

1/4

P (B) =

{20}/{100}

1/5

P (C) =

{10}/{100}

1/{10}

Now, required probability =

1/2×14+3/{10}×1/5+1/5×1/{10}

1/8+3/{50}+1/{50}

{50+24+8}/{400}

{82}/{400}

= 0.205

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