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GUJCET 2025 Math Paper

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Question : 7 of 40

Marks: +1, -0

Two events

E

F

are independent. If

P(E) = \frac{3}{5}

P(F) = \frac{3}{10}

P(E'/F) + P(F'/E) = \text{ . . . . . . }

$\frac{1}{10}$
$\frac{11}{10}$
$\frac{9}{10}$
$\frac{10}{11}$

Solution:

Concept:

For independent events, complements are also independent, so

P(E'/F)=P(E')

and

P(F'/E)=P(F')

.

Explanation:

Given

P(E)=\frac{3}{5}

and

P(F)=\frac{3}{10}

.

Since

E

and

F

are independent,

E'

and

F

are independent.

So,

P(E'/F)=P(E')=1-P(E)=1-\frac{3}{5}=\frac{2}{5}

.

Similarly,

P(F'/E)=P(F')=1-P(F)=1-\frac{3}{10}=\frac{7}{10}

.

Now add them:

P(E'/F)+P(F'/E)=\frac{2}{5}+\frac{7}{10}

.

Convert:

\frac{2}{5}=\frac{4}{10}

.

Thus,

\frac{4}{10}+\frac{7}{10}=\frac{11}{10}

.

Answer:

\frac{11}{10}

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