Originally Posted by

**jickjoker** **just thought i would go on a few sites and pratice some Binomial Distribution questions**

**i found these on tutorvista , is it me or are all the answers given wrong**

**Examples for Application of Binomial Disrtibution:**

**Example 1:**

A die is tossed 4 times. What is the Probability of getting exactly 3 fours?

**Solution:**

Here n = 4, x = 3, probability of success on a single trial = 1/ 4 or 0.25.

Therefore, The binomial probability is,

p(X =r) = ncr pr q(n-r) where p + q=1 then q =1-p

q=1-0.25

q=0.75

b( 3; 4, 0.25 ) = 4C3 × ( 0.25)3 × ( 0.75)4 −3

= ( 4! / 3! × (4-3)!) × 0.016 × ( 0.75)

= (4! / 3! × 1!) × 0.016× 0.75

= 4 × 0.016 × 0.75

b( 3; 4, 0.25 ) = 0.048. Answer.

**Example 2:**

A die is tossed 7 times. What is the Probability of getting exactly 5 twos?

**Solution:**

Here n = 7, x = 5, probability of success on a single trial = 1/ 7 or 0.143.

Therefore, The binomial probability is,

p(X =r) = ncr pr q(n-r) where p + q=1 then q =1-p

q=1-0.143

q=0.857

b( 5; 7, 0.143 ) = 7C5 × ( 0.143)5 × ( 0.857)7 −5

= ( 7! / 5! × (7-5)!) × (0.0001) × ( 0.857)2

= (7! / 5! × 2!) × 0.0001× 0.734

= 21 ×0.0001 × 0.734

b( 5; 7, 0.143 ) = 0.00154. Answer.

**Practice Problems for Application of Binomial Distribution:**

1 A die is tossed 2 times. What is the Probability of getting exactly 1sixes?

1) 0.5.