Question

20) A card is drawn from a deck and then replaced. Then a second card is drawn. find the probability of getting an ace both times.

21) A coin is tossed and then a die is rolled. Find the probabilty of getting a 5 on the die given that the coin landed tails up.

Answer 1

Here' the answer to the question. please write back in case you've doubts.

20)

P(both ace) = ?

Remember this is draws with replacement, so events are independent.

Also, there are 4 Aces in a pack of 52 cards, so P(get a Ace on a draw) = 4/52

So, P(getting ace both times) = (4/52)*(4/52) = 0.0059

21)

Again, rolling a die is indepenent of tossing a coin.

So, given that the coin rolled tails ( which happens with .5 probability), the chances of getting 5 is ?

P(getting any number on a fair dice) = 1/6 , as there are 6 numbers on a dice with each number getting a 1/6 probability to show up.

P(getting a 5 on the die given the coin landed tails up)

= P(coin gives tail)*P(get 5 on dice)/P(coin gives tail)

= (1/2)*(1/6)/ ( 1/2)

= 1/6