a bag contains 11 coloured balls 8 of which are blue if a ball is drawn at random from the bag 6

A bag contains 11 coloured balls 8 of which are blue if a...

A bag contains 11 colored balls, 8 of which are blue. If a ball is drawn at random from the bag 6 times, with replacement, what is the probability of drawing exactly five blue balls? A. (8/11)^5 B. (8/11)^5 * (3/11) C. (8/11)^5 * (3/11) D. (8/11)^5 * (3/11) E. 1 - (3/11)^5 Sara fires 14 arrows at an archery target that has a yellow bullseye, an inner red ring, and an outer blue ring. If each shot has a 25% chance of hitting the bullseye, a 15% chance of hitting the inner ring, and a 60% chance of hitting the outer ring, find the probability that 4 of Sara's shots are bullseyes, 5 land in the inner ring, and 5 land in the outer ring. A. (14 choose 4) * (0.25)^4 * (0.15)^5 * (0.6)^5 B. (14 choose 4) * (0.25)^4 * (0.15)^5 * (0.6)^5 C. (14 choose 4) * (0.25)^4 * (0.15)^5 D. (14 choose 4) * (1.05)^5 * (0.55)^5 E. (0.25)^4 + (0.15)^5 + (0.6)^5

Transcript

00:01 In this problem, we have two questions.

00:03 For the first question, we have 11 colored balls of which 8 are blue.

00:10 We are also given that a ball is drawn with replacement six times.

00:14 We want to find the probability that exactly five balls are blue in the drawers.

00:23 Now, since we know that there are 8 out of 11 blue balls, so the probability of getting a blue ball in the, a draw is 8 out of 11.

00:38 But since there are six draws, so of which five we want to be blue balls, so there are actually six times, of which we choose five times to be blue.

00:54 So it's six choose five.

00:56 And so each time we want the blue ball is 8 out of 11, but it's drawn five times.

01:02 So it's 8 out of 11 times 8 out of 11 times.

01:06 8 out 11 5 times so it will be to the power of 5 and then the other ball that is drawn would be not a blue ball so not a blue ball would be 3 out 11 so it will be 3 out 11 but only one time so this would be the answer so b is the answer now let's look at the next question 14 arrows are fired at a target that is a 25 % chance of hitting a blue eyes that means the boos eye that means the probability of a blue eye is 0 .25 and a 15 % chance of hitting an inner ring means this will be 0 .15 for the inner ring and 60 % chance of hitting the outer ring that means 0 .6 now we want to find the probability that the four shots are bull's eyes.

02:15 Five will land in the inner ring and five will land in the outer ring.

02:22 Now, since there are 14 shots, so it would be for four shots to be bull's eyes, that means i need to take 14 choose four to be the bull's eyes.

02:33 Now, boo's eyes is each shot is 0 .25.

02:37 Now, since there are four shots, it will be 0 .25 times 0 .25 .25.

02:42 Times 0 .25 times 0 .25 to the power of.

02:49 Now next one, it will be 5 shots landing in the inner ring...