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One card is drawn at random from a well-...

One card is drawn at random from a well-shuffled deck of 52 playing cards. Find the probability that the card drawn is neither a red card nor a queen.

A

`2/13`

B

`6/13`

C

`5/13`

D

`8/13`

Text Solution

Verified by Experts

The correct Answer is:
B
Total number of all possible outcomes = 52.
(i) Let `E_(1) ` be the event of getting a red card or a king.
There are 26 red cards (including 2 kings) and there are 2 more kings.
So, the number of favourable outcomes = ` 26+ 2 = 28`.
`:. ` P(getting a red card or a king) ` = P(E_(1)) = 28/52 = 7/ 13`.
(ii) Let `E_(1)` be the event of getting a card which is neither a red card nor a queen.
There are 26 red cards (including 2 queens) and there are 2 more queens. So, the number of non-favourable outcomes = 26+2 = 28.
`:. ` the number of favourable outcomes = 52 - 28 = 24.
`:. ` P(getting neither a red card nor a queen) = ` 24/ 52 = 6/ 13`.
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