Mathematics, 09.12.2019 15:31 Christiancameron1234

Select all that apply.

for two events a and b, p(a) = 0.5, p(b) = 0.35, and p(a/b) = 0.7. select all of the correct statements.

a. p(b/a) = 0.49
b. p(b/a) = p(a/b)
c. p(a ∩ b) = 0.245
d. p(a ∩ b) = 0.35

Answers: 2

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Answers

Answer from: sonnyboi2305

a. P(B/A) = 0.49

c. P(A ∩ B) = 0.245

Step-by-step explanation:

We know that for any dependent events A and B, the conditional probability of getting A given that B is given by :-

$P(A|B)=\dfrac{P(A\cap B)}{P(B)}$

Given: P(A) = 0.5, P(B) = 0.35, and P(A/B) = 0.7

$\\\Rightarrow\ 0.7=\dfrac{P(\cap B)}{0.35}\\\\\Rightarrow\ P(A\cap B)=0.35\times0.7=0.245$

Now, the conditional probability of getting B given that A is given by :-

$P(B|A)=\dfrac{P(A\cap B)}{P(A)}\\\\\Rightarrow\ P(B|A)=\dfrac{0.245}{0.5}=0.49\neq P(A|B)$

Hence, the correct statements are :

a. P(B/A) = 0.49

c. P(A ∩ B) = 0.245

Answer from: Quest

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

Me? ! with this question which relationship is a function?

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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