Help Me PLEASE!!!

Mathematics

1 answer:

lesya692 [45]4 years ago

7 0

Answer:

P = 0.5207

Step-by-step explanation:

First, we have three options: Just the first card is a diamond or an ace, Just the second card is a diamond or an ace and both cards are diamonds or aces.

Additionally, there are 16 cards that are diamond or aces in a standard deck of 52 cards (13 diamonds and 3 aces that are not diamonds). It means that there are 36 cards that are not diamond or aces (52 - 16 = 36).

So, the probability that just the first card is a diamond or an ace is calculated as:

$P_1=\frac{16}{52}*\frac{36}{52}=0.2130$

At the same way, the probability that just the second card is a diamond or an ace is:

$P_2=\frac{36}{52}*\frac{16}{52}=0.2130$

Finally, the probability that both cards are diamonds or aces is:

$P_3=\frac{16}{52}*\frac{16}{52}=0.0947$

Therefore, the probability that at least one of the cards is a diamond or an ace is:

$P=P_1+P_2+P_3\\P=0.2130+0.2130+0.0947\\P=0.5207$

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