Assertion (A) : If a box contains 5 white, 2 red and 4 black marbles, then the probability of not drawing a white marble from the box is 5/11. Reason (R) : P(E ?)=1-P

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Solution

Q.
Assertion (A) : If a box contains 5 white, 2 red and 4 black marbles, then the probability of not drawing a white marble from the box is 5/11.

Reason (R) : $P (E) = 1 - P (E),$ where E is any event.

1 Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)

2 Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3 Assertion (A) is true but Reason (R) is false.

4 Assertion (A) is false but Reason (R) is true.

Ans.
(4)

Given, a box contains 5 white, 2 red and 4 black marbles.

Total number of marbles =5+2+4=11

Let E be the event of drawing a white marble.

$P (E) = \frac{N u m b e r o f w h i t e m a r b l e s}{T o t a l n u m b e r o f m a r b l e s} = \frac{5}{11} W e k n o w t h a t P (E) + P (E) = 1 \Rightarrow P (E) = 1 - P (E) \Rightarrow P (N o t d r a w i n g a w h i t e m a r b l e) = 1 - P (D r a w i n g a w h i t e m a r b l e) P (E) = 1 - \frac{5}{11} = \frac{6}{11}$

Therefore, Assertion (A) is false but Reason (R) is true.

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