Question

A group of friends wanted to play cards with two identical packs together. While shuffling the cards, three cards are dropped. Rest of the cards are shuffled and one card is drawn at random. Assuming that the dropped cards were a queen of hearts, a ten of spades and an ace of clubs, answer the following questions:

1. Find the probability that the drawn card is a face card.   [1]
2. Find the probability that the drawn card is either a king or a queen.   [1]
3. 1. Do you think that the probability of getting a queen was higher if none of the cards were dropped? Justify your answer.   [2]
                                                      OR
   2. Find the probability that the drawn card is a jack. Compare it with the probability when none of the cards were dropped. In which case is the probability of getting a jack higher?   [2]

Answer 1

Given: Two identical packs of cards = 52 × 2

= 104

Three cards are dropped = 104 − 3

= 101

(i) Probability that the drawn card is a face card

Face cards in two packs = 24

Dropped face cards = Queen of Hearts (1 card)

Remaining face cards = 24 − 1

= 23

Probability (drawn card is face card) = `"Number of favorable outcomes"/"Total outcomes" = 23/101`

(ii) Kings in two packs = 8 (4 per pack × 2)

Queens in two packs = 8

Dropped Queen of Hearts = 1

Remaining Queens = 8 − 1

= 7

Total favorable cards (Kings or Queens)

= 8 (Kings) + 7 (Queens)

= 15

Probability (drawn card is King or Queen) = `15/101`

(iii) (a) If no cards were dropped, total cards = 104

Number of Queens in two packs = 8

Probability of drawing a Queen when no cards dropped = `8/104` 

= `2/26`

= `1/13`

Probability of drawing a Queen when one Queen of Hearts is dropped: 

Probability = `7/101`

Compare the two probabilities: 

Since `1/13 > 7/101`, the probability of getting a Queen was higher if none of the cards were dropped.

                                         OR

(iii) (b) Number of Jacks in two packs = 8 (4 per pack × 2) 

Probability (drawn card is Jack) = `8/101`

If no cards were dropped, total cards = 104

Probability (drawn card is Jack)

= `8/104 `

= `2/26` 

= `1/13`

Compare the two probabilities:

`8/101 > 1/13`

The probability of getting a jack is higher after the cards were dropped.