Question 2 3 pts It is known that that 70% of females and...

Question 2 3 pts It is known that that 70% of females and 60% of males react positively to a set of circumstances. A group of 25 people, 10 females and 15 males, were subjected to the circumstances, and they were asked to describe their reactions to a written questionnaire. A response is randomly picked from the group and is negative. What is the probability that the response is from a male? Note: Round your answer to four decimal places. ? 0.3333 ? 0.5294 ? 0.4706 ? 0.6667

Transcript

00:01 Males and females are observed to react differently to a given set of circumstances.

00:06 It's been observed that 70 % of the females react positively to these circumstances where only 40 % of the males react positively.

00:15 Of the 20 people, 15 females and 5 males were subjected to these circumstances and they were asked to describe their reactions.

00:25 Find the probability that a response picked randomly from the 20 is now.

00:30 So i'm going to start.

00:32 I've started a tree diagram here and i want to know male, female, what's the probability of actually picking a male versus a female? so the probability of a female is going to be 15 out of 20.

00:47 And a probability of a male is going to be 5 out of 20.

00:52 Since we have the other in percentages which we're going to convert to decimals, i'm going to go ahead and put these as a decimal.

01:00 So 15 divided by 20 is going to be 0 .75, and this will be 0 .25.

01:07 So the probability of a female is 0 .75, which i'm going to put here, 0 .75, and the male is 0 .25, which i'll put here.

01:18 Now i'm going to go back to my question, and it says 40 % of the males react positively.

01:24 So that's going to be a 40 % going to the positive, which means we're going to have 60 % going.

01:30 To the negative.

01:32 Then for the females it says 70 % react positively, and therefore we're going to have 30 % negatively.

01:40 Now that we have this information, we can see what we need.

01:44 So i'm going to come over here and get my black pen back.

01:49 So we want to know the probability of a negative.

01:52 Probability of a negative...

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