1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# From a pack of 52 playing cards jacks, queens, kings and aces of red colour are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn is(i) a black queen (ii) a red card (iii) a black jack (iv) a picture card (Jacks, queens and kings are picture cards)

Open in App
Solution

## Total no. of cards in a pack =52After removing red-colored - jack, queen, king, and aces,No. of cards =52−8=44 andNo. of red cards =26−8=18.Solution(i):No. of black queens =2Therefore, 2C1( Selecting 1 out of 2 items) times out of 44C1( Selecting 1 out of 44 items) a black queen is picked.Let E be the event of getting a black queen from packWe know that, Probability P(E) =(No.of favorable outcomes)(Total no.of possible outcomes)=2C144C1=244=122Solution(ii):No. of red cards =18Therefore, 18C1( Selecting 1 out of 18 items) times out of 44C1( Selecting 1 out of 44 items) a red card is picked.Let E be the event of getting a red card from the packWe know that, Probability P(E) =(No.of favorable outcomes)(Total no.of possible outcomes)=18C144C1=1844=922Solution(iii):No. of black jack cards =2Therefore, 2C1( Selecting 1 out of 2 items) times out of 44C1( Selecting 1 out of 44 items) a black jack card is picked.Let E be the event of getting a black jack card from the packWe know that, Probability P(E) =(No.of favorable outcomes)(Total no.of possible outcomes)=2C144C1=244=122Solution(iv):No. of picture cards =12−6=6 ..... (As red cards are removed and there are 6 red picture cards )Therefore, 6C1( Selecting 1 out of 6 items) times out of 44C1( Selecting 1 out of 44 items) a picture card is picked.Let E be the event of getting a picture card from packWe know that, Probability P(E) =(No.of favorable outcomes)(Total no.of possible outcomes)=6C144C1=644=322

Suggest Corrections
1
Join BYJU'S Learning Program
Related Videos
Operations on Sets
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program