Topic:C<span>onditional Probability
</span>For any two events A and B, where P(B) ≠ 0, P( A | B ) = P( A ∩ B ) / P( B ) = P( B | A) * P(A) / P(B)..i.e..{the probability of A given B is equal to the probability of A and B divided by the probability of B}
<span>For a set of events A1, A2, A3, ... , An,
</span>hence,
P(B)
<span>= P(B and A1) + P(B and A2) + ... + P(B and An) </span>
= P(B | A1) * P(A1) + P(B | A2) * P(A2) + ... + P(B | An) * P(An)
P(M | N)
<span>= P(N | M) * P(M) / P(N) </span>
<span>= P(N | M) * P(M) / (P(N | M) * P(M) + P(N | M') * (1 - P(M)))
</span><span>Substitute Values.... you get ?
</span>
Answer:
The answer is 1800.
Step-by-step explanation:
3/540 = 10/x
3x = 540 × 10
x = 5400/3
x = 1800
Answer:
Mike gets just one cookie because she puts 18 cookies in 19 box which will be 19*18 = 342 so just one left
Step-by-step explanation:
I'm feeling bad for Mike to be honest that he just gets one
Answer:
<h3>Graph 3</h3>
Line starting at x = -2
- <u>Domain</u>: x ≥ -2
- <u>Range</u>: y ≥ 0
<h3>Graph 4</h3>
Vertical line
- <u>Domain</u>: x = 3
- <u>Range</u>: y = any real number
<h3>Graph 5</h3>
Quadratic function with negative leading coefficient and max value of 3
- <u>Domain</u>: x = any real number
- <u>Range</u>: y ≤ 3
<h3>Graph 6</h3>
Curve with non-negative domain and min value of -2
- <u>Domain</u>: x ≥ 0
- <u>Range</u>: y ≥ -2
<h3>Graph 7</h3>
Line with no restriction
- <u>Domain</u>: x = any real number
- <u>Range</u>: y = any real number
<h3>Graph 8</h3>
Quadratic function with positive leading coefficient and min value of 4
- <u>Domain</u>: x = any real number
- <u>Range</u>: y ≥ 4
<h3>Graph 9</h3>
Parabola with restriction at x = -4
- <u>Domain</u>: x = any real number except -4
- <u>Range</u>: y = any real number
<h3>Graph 10</h3>
Square root function with star point (2, 0)
- <u>Domain</u>: x ≥ 2
- <u>Range</u>: y ≥ 0
k, n - integers
2k+1 - an odd integer
2n+1 - another odd integer
The product of them:
(2k + 1)(2n + 1) =
= 4kn + 2k + 2n + 1 =
= 2(2kn + k + n) + 1
The product of integers (2kn) is integer
and the sum of them (2kn+k+n) also is integer
So (2k + 1)(2n + 1) = 2(2kn + k + n) + 1 is an odd integer