I have a large jar of red and green M&amp;M’s with 55% red M&amp;M’s. I plan to pick 7 M&amp;M’s. 1. I want to find the probability that I get 2 red M&amp;M’s out of 7. a) How many different ways can you get 2 red M&amp;Ms out of 7? Use the formula for the binomial coefficient to find that number. b) Use your answer from (d) and the binomial formula to calculate the probability that you get 2 red M&amp;M’s out of 7. c) Use your calculator to find the probability that I get 3 red candies out of the 7 picked

Question

I have a large jar of red and green M&amp;amp;M’s with 55% red M&amp;amp;M’s. I plan to pick 7 M&amp;amp;M’s.   1. I want to find the probability that I get 2 red M&amp;amp;M’s out of 7.   a) How many different ways can you get 2 red M&amp;amp;Ms out of 7? Use the formula for the binomial coefficient to find that number.   b) Use your answer from (d) and the binomial formula to calculate the probability that you get 2 red M&amp;amp;M’s out of 7.   c) Use your calculator to find the probability that I get 3 red candies out of the 7 picked

Alara Mccarthy · Accepted Answer

Step 1 The binomial coefficient is computed by (nk)=n!k!(n−k)! which gives the number of ways to select k objects from n objects. Here it is asked to find the number of ways to draw 2 red candy out of 7, so substitute n=7 and k=2 in the formula of binomial coefficient. Number of ways =(72) =7!2!(7−2)! =7⋅6⋅5!2⋅5! =21 Step 2 The probability of binomial random variable is computed by formula p(k)=(nk)pk(1−p)n−k, where n is the total number of trials, k is the number of successes and p is the probability of success in each trial. In each trial, the probability of getting red candy is 55% or 0.55 and there are total 7 trails out of which 2 should be successful (drawn red). So substitute n=7,k=2 and p=0.55 in the formula of binomial probability. P(2)=(72)(0.55)2(1−0.55)7−2 =21⋅0.3025⋅0.455 ≈0.1172 Step 3 For the case of 3 red candies out of 7, the total number of trials are n=7, number of successes are k=3 and probability of success is p=0.55. To find the probability of 3 successes, follow the steps mentioned below on the calculator. 1. Select 2nd and VARS on the calculator. 2. There will be lift of different distributions, select binompdf() that means binomial probability density function. 3. Then enter the parameters in this sequence 7, 0.55, 3 4. Then press Enter. This will gives the probability of getting 3 red candies out of 7 which is equal to 0.2388.

I have a large jar of red and green M&M’s with 55% red M&M’s. I plan to pick 7 M

Answered question

Answer & Explanation

New Questions in High school probability