4 because there’s usually only 4 answers
Answer: I think it’s C sorry if it’s not
Step-by-step explanation:
The probability of an event A occurring given that B has occurred is
P(A | B) = P(A and B) / P(B)
a. By the definition above,
P(spade | black) = P(spade and black) / P(black)
- P(black) = 26/52 = 1/2 because 26 of the 52 cards have a black suit
- All spade cards are black, so P(spade and black) = P(spade) = 13/52 = 1/4
Then P(spade | black) = (1/4) / (1/2) = 1/8.
b. We can do the same breakdown as in (a), or we can make use of the definition of conditional probability
P(A | B) = P(A and B) / P(B) = (P(B | A) * P(A)) / P(B)
Then
P(black | spade) = (P(spade | black) * P(black)) / P(spade)
- P(black) = 1/2
- P(spade) = 1/4
- P(spade | black) = 1/8
Then P(black | spade) = (1/8 * 1/2) / (1/4) = 1/64.
c. By definition,
P(7 | black) = P(7 and black) / P(black)
- P(7 and black) = 1/52 because this is a unique card
- P(black) = 1/2
Then P(7 | black) = (1/52) / (1/2) = 1/104.
d. By definition,
P(king | face) = P(king and face) / P(face)
- All kings are face cards, so P(king and face) = P(king) = 4/52 = 1/13
- P(face) = 12/52 = 3/13
Then P(king | face) = (1/13) / (3/13) = 1/3.
Answer:
*Note c could be written as a/b
Step-by-step explanation:
-sin(-t - 8 π) + cos(-t - 2 π) + tan(-t - 5 π)
The identities I'm about to apply:
Let's apply the difference identities to all three terms:
We are about to use that cos(even*pi) is 1 and sin(even*pi) is 0 so tan(odd*pi)=0:
Cleaning up the algebra:
Cleaning up more algebra:
Applying that sine and tangent is odd while cosine is even. That is,
sin(-x)=-sin(x) and tan(-x)=-tan(x) while cos(-x)=cos(x):
Making the substitution the problem wanted us to:
Just for fun you could have wrote c as a/b too since tangent=sine/cosine.
Answer:
A is the correct answer to your question