Is about the assignment chapter 5 basic probability question 15

Question

A ball is drawn randomly from a jar that contains 3 red balls, 5 white balls, and 7 yellow ball. Find the probability of the given event.

(a) A red ball is drawn;

The probability is :   

(b) A white ball is drawn;

The probability is :   

(c) A yellow ball is drawn;

The probability is : 

Answer 1

3R, 5W, 7Y

a) P(R) = 3/(3+5+7) = 3/15 = 1/5 = 20% propability of red

b) P(W) = 5/(15) = 1/3 = 33 1/3% probability of white

c) P(Y) = 7/15 = 0.4666... = 46 2/3% probability of yellow

20+33 1/3 + 46 2/3 = 100%

that assumes the random drawings are with replacement, or just independent events

without replacement, in order Red, White, then Yellow

a) P(R) = 1/5 = 20% chance of Red on 1st draw

b) P(W) = 5/14 = 0.3571428571428571428... = about 35.7% chance of White on 2nd draw

c) P(Y) = 7/13 = 53.8% chance of Yellow on 3rd draw

these 3 probabilities do not sum to 100%

Answer 2

There are 15 total balls so:

The probability of drawing a red ball is 3/15 which is the same as 1/5 or 20%

The probability of drawing a white ball is 5/15 which is the same as 1/3 or 33 1/3%

The probability of drawing a yellow ball is 7/15 which is the same as 46 2/3%

Answer 3

So in my response to this question, I'll just take care of part (a) because parts (b) and (c) will follow similarly in set-up and process.

We see that the problem shares the number of each type of color ball in this jar, and in order to find the probability (via classical probability) we need to know the total sample space, which comes from adding up all the colored balls in the jar.

Then we'll use the following simple formula for classical probability:

number of focused events/items

total sample space

Sample space = 15 total balls

Therefore, the probability of a red ball drawn = 3 / 15 = 1 / 5

This means that, given one drawing (selection) from the jar, the chance of pulling out any of those red balls is 1/5 - and every red ball has this same probability/chance.

Answer 4

A ball is drawn randomly from a jar that contains 3 red balls, 5 white balls, and 7 yellow ball. Find the probability of the given event.

(a) A red ball is drawn;

The probability is :   

(b) A white ball is drawn;

The probability is :   

(c) A yellow ball is drawn;

The probability is : 

Probability is a ratio, comparing the event of interest to all possible outcomes. All possible outcomes here are 3 red balls + 5 white balls + 7 yellow balls = 15 total balls in the jar.

P(red ball) = # red balls / # total balls = 3 / 15 = 1/5 or 0.2

P(white ball) = # white balls / # total balls = 5 / 15 = 1/3 or 0.3333...

P(yellow ball) = # yellow balls / # total balls = 7 / 15 = or 4666...

Hope this helps