You are shown five cards, Three have X written on them and two have Y. The cards are turned over so the X abd Y are no longer visible, and shuffled/ One card is picked and laid face up on the table. It is an X.

Question

If the remaining cards are shuffled and another card is now laid on the table:
a) What do you expect this card to be?
b) Find the probability that this card is X

1. If in the eg. above, the card is turned up is a Y, and if the remaining cards are shuffled and another card is now laid on the table:
a) What do you expect this card to be?
b) Fins the probability that the card is X.

2. Two dice are rolled at the same time. Find the probabilty that
a) the 2nd die shows a 5, given that the first die showed a 5.
b) The sum is 6, given that the first die showed a 5.
c) the first die showed a 5, given that the sum is 6.

3A) A two digit no. is written down. Find the probability that
a) it is palindromic, given that the unit digit is a 5.
b) It is palindormic, given that the tens digit is a 5.
c) The unit digit is a 5, given that the tens digit is a 3.
d) It is divisible by 9, given that the tens digit is a 3.
e) The tens digit is a 3, given that it is divisible by 9.

4. Malcolm buys 4 tickets in a raffle in which 50 tickets are sold. Tickets are drawn for 1st and 2nd prizes.
a) What is the probability of Malcolm wining the first prize?
b) Work out what is the probability of him wining the second prize, given that he wins the first.
c) Find the probability of winning the second prize, given that Malcolm does not win 1st prize.

5. A card is selected from a 52 card pack. Find the probability that the card is :
a) a Jack, given that the card is a picture card,
b) a Heart, given that the card selected is red.

Answer 1

We do not do your homework for you. However, I will give you a start.

1ab) Among the remaining 4 cards, there are 2 X's and 2 Y's.

I hope this helps.