Question

One card is drawn at random from a well-shuffled deck of 52 plagying cards. Find the probability that the card drawn is (i) either a red card or a king, (ii) neither a red card nor a queen. Select the correct answer from above options

Answer 1

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`.