Answer:
Hey there!
There are 13 clubs in a deck of cards.
There are 4 tens.
However, the tens overlap with the clubs, so there are 16 cards to choose.
16/52=4/13
Let me know if this helps :)
The events are mutually inclusive. Option B is correct because the required probability is [tex]\dfrac{4}{13}[/tex].
Important information:
A deck of cards has total 52 cards, which includes 4 suits and each suit has 13 cards. If S be the sample space, then n(S) = 52.
Let A be the event that the card is a club card and B be the event that it is a ten card.
The number of club cards is 13. So, n(A) = 13.
There are 4 cards of 10. So, n(B) = 4.
One ten card is of club. So, [tex]n(A\cap B)=1[/tex].
Since [tex]n(A\cap B)=1\neq 0[/tex], therefore the events are mutually inclusive.
The number of club or a ten card is:
[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]
[tex]n(A\cup B)=13+4-1[/tex]
[tex]n(A\cup B)=16[/tex]
Now,
[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]
[tex]P(A\cup B)=\dfrac{16}{52}[/tex]
[tex]P(A\cup B)=\dfrac{4}{13}[/tex]
Therefore, the probability of choosing a card from a deck of cards that is a club or a ten is [tex]\dfrac{4}{13}[/tex]. Hence, option B is correct.
Find out more about 'Probability' here:
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