## Christa randomly selects two cards with, replacement, from a normal deck of cards. Calculate the possibility the first card is a 6 of spades

Question

Christa randomly selects two cards with, replacement, from a normal deck of cards. Calculate the possibility the first card is a 6 of spades and the second is a 8 of clubs

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1 day 2021-09-10T04:30:37+00:00 1 Answer 0

1. Answer: The probability that the first card and second card that Christa selects WITH replacement will be a “6” of spade and an “8” of club respectively is 1/2704 or 0.0003698

Step-by-step explanation:

Since Christa is picking up the game cards from a normal deck of cards, we assume that the cards were picked from a deck of 52 complete cards.

A club contains a total of 13 cards and a spade contains a total of 13 cards as well.

The next step is to find the probability of picking up a 6 of spade alone from the complete deck of cards. Since there is only one “6” of spade in the entire deck of 52 cards, then the probability of picking it up = 1/52

Similarly, there is just one “8” of club in the entire deck of 52 cards, so the probability that it will be picked up is 1/52

Then, if Christa proceeds to select 2 cards WITH replacement from the deck of 52 game cards, the probability that the first card is a “6” of spades and the second card is an “8” of club:

= [1/52] × [1/52] (since it’s WITH replacement)

= 1/2704

Therefore the probability that the first card is a “6” of spades and the second card is an “8” of club is 1/2704 or 0.0003698