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
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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**

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