Question

A board game uses the deck of 20 cardsshown to the right. Two cards are selectedat random from this deck. Determine theprobability that neither card shows a 3, bothwith and without replacement1 2 3 4 5N285Determine the probability that neither card shows a 3, with replacement.(Type an integer or a simplified fraction.)Determine the probability that neither card shows a 3, without replacement(Type an integer or a simplified fraction.)

Answer 1

The probability without replacement means that the total number of outcomes decreases by 1 after each selection. Also, we have to multiply the probability of each attempt.

`P=(16)/(20)\cdot(15)/(19)`

Observe, that the first attempt includes 16 possible events because there are 16 cards without 3, then, the second attempt includes 15 possibles and 19 total outcomes, that's because the card we selected first is not present in the deck.

`P=(16*15)/(20*19)=(240)/(380)=(12)/(19)`

Hence, the probability of not getting a 3, without replacement is 12/19.

On the other hand, the probability with replacement is

`P=(16)/(20)\cdot(16)/(20)=(16*16)/(20*20)=(256)/(400)=(64)/(100)=(32)/(50)=(16)/(25)`

Hence, the probability of not getting a 3, with replacement, is 16/25.