Answer:
72.4%
Step-by-step explanation:
The probability of A occurring given that B occurs = the probability of both A and B / the probability of B
P(A|B) = P(A∩B) / P(B)
This can be rearranged as:
P(A∩B) = P(B) P(A|B)
In this case:
A = biased coin is chosen
~A = fair coin is chosen
B = 4 heads then 1 tail
First, let's find P(A∩B).
P(A∩B) = P(B) P(A|B)
P(A∩B) = ½ × ₅C₄ (⅘)⁴ (⅕)¹
P(A∩B) = 0.2048
Next, find P(~A∩B).
P(~A∩B) = P(B) P(~A|B)
P(~A∩B) = ½ × ₅C₄ (½)⁴ (½)¹
P(~A∩B) = 0.078125
Therefore, the probability that the coin is biased is:
P = P(A∩B) / (P(A∩B) + P(~A∩B))
P = 0.2048 / (0.2048 + 0.078125)
P = 0.723866749
The probability is approximately 72.4%.
Answer:
"13 / 204 ; No, they are dependent events
"
Step-by-step explanation:
The probability of getting a club at first throw is simply total number of clubs divided by total number of cards in the deck.
Total clubs is 13
Total cards in deck is 52
Hence, P(clubs) = 
<em>Since the first card IS NOT replaced, the deck has now 51 cards. We want probability of diamond. There are still 13 diamonds, so probability of diamond now would be 13/51</em>
<em />
Hence, Probability that first card is a club and the second card is a diamond should be 13/52 MULTIPLIED by 13/51
P(1st Club, 2nd Diamond) = 
<u></u>
<u>Note: </u>They are dependent events since we are calculating probability without replacement. The first draw affected the total number of cards in the 2nd draw.
2nd answer choice is right.
Answer:
second option
Step-by-step explanation:
Given
+ 6x² + 5 = 0
let u = x², then
u² + 6u + 5 = 0 ← in standard form
(u + 1)(u + 5) = 0 ← in factored form
Equate each factor to zero and solve for u
u + 1 = 0 ⇒ u = - 1
u + 5 = 0 ⇒ u = - 5
Change u back into terms of x, that is
x² = - 1 ( take the square root of both sides )
x = ±
= ± i ( noting that
= i ), and
x² = - 5 ( take the square root of both sides )
x = ±
= ±
= ±
×
= ± i
Solutions are x = ± i and x = ± i
Answer: If two pair is parallel then it has no solution.
Step-by-step explanation:
Since we have given that
Let the number of gained yards by each player be y
For the case of Brayden:
Equation will be

For the case of Howard :
Equation will be

For the case of Vincent :

Since First two equations are parallel so it has no solution.
Reason:

Hence, if two pair is parallel then it has no solution.