PLS HELP ASAP Given the following probabilities, for what P(B) are events A and B independent? P(A)=23 P(A and B)=13

I'm assuming you meant to say

P(A) = 2/3

P(A and B) = 1/3

If that is the case, then A and B are independent if and only if the following equation is true

P(A and B) = P(A)*P(B)

So we multiply P(A) and P(B) to get the value of P(A and B). We don't know what P(B) is, but we can use algebra to find it

P(A and B) = P(A)*P(B)

P(A)*P(B) = P(A and B)

(2/3)*P(B) = 1/3

P(B) = (1/3)*(3/2) multiply both sides by the reciprocal of 2/3

P(B) = (1*3)/(3*2)

If P(B) = 1/2, then

P(A and B) = P(A)*P(B)

P(A and B) = (2/3)*(1/2)

P(A and B) = (2*1)/(3*2)

P(A and B) = 1/3

Which is the given probability for both events happening. This confirms we have the correct P(B) value.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.