CK-12-Basic Probability and Statistics Concepts - A Full Course

4.4. Binomcdf Function http://www.ck12.org

A success is using a card. We are interested in at most 5 people using a card. That is, we are interested in 0, 1, 2, 3,
4, or 5 people using a card. Therefore,a= 5 , 4 , 3 , 2 , 1 ,and 0.

The probability of a success is 40%, or 0.40, and, thus,p= 0 .40.

Therefore, the probability of a failure is 1− 0 .40, or 0.60. From this, you know thatq= 0 .60.

P(X=a) =nCa×pa×q(n−a)

P(5 people using a card) = 10 C 5 ×p^5 ×q^5

P(5 people using a card) = 10 C 5 ×( 0. 40 )^5 ×( 0. 60 )^5

P(5 people using a card) = 252 × 0. 01024 × 0. 07776

P(5 people using a card) = 0. 201

P(4 people using a card) = 10 C 4 ×p^4 ×q^6

P(4 people using a card) = 10 C 4 ×( 0. 40 )^4 ×( 0. 60 )^6

P(4 people using a card) = 210 × 0. 0256 × 0. 04666

P(4 people using a card) = 0. 251

P(3 people using a card) = 10 C 3 ×p^3 ×q^7

P(3 people using a card) = 10 C 3 ×( 0. 40 )^3 ×( 0. 60 )^7

P(3 people using a card) = 120 × 0. 064 × 0. 02799

P(3 people using a card) = 0. 215

P(2 people using a card) = 10 C 2 ×p^2 ×q^8

P(2 people using a card) = 10 C 2 ×( 0. 40 )^2 ×( 0. 60 )^8

P(2 people using a card) = 45 × 0. 16 × 0. 01680

P(2 people using a card) = 0. 121

P(1 person using a card) = 10 C 1 ×p^1 ×q^9

P(1 person using a card) = 10 C 1 ×( 0. 40 )^1 ×( 0. 60 )^9

P(1 person using a card) = 10 × 0. 40 × 0. 01008

P(1 person using a card) = 0. 0403

P(0 people using a card) = 10 C 0 ×p^0 ×q^10

P(0 people using a card) = 10 C 0 ×( 0. 40 )^0 ×( 0. 60 )^10

P(0 people using a card) = 1 × 1 × 0. 00605

P(0 people using a card) = 0. 00605