Ryan spent a dollar on a Tri-State Megabucks ticket, enticed by a big jackpot. Ryan chose six different numbers from 1 to 40, inclusive, hoping that they would be chosen later during the TV drawing. Sad to say, none of Ryan’s choices were drawn. What was the probability of this happening? The order in which numbers are drawn is of no significance.
Accepted Solution
A:
Answer: 0.8591Step-by-step explanation:Given : Total numbers in the jackpot : 40Then the probability of getting jackpot = [tex]\dfrac{1}{40}=0.025[/tex]Using binomial probability formula :-[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]If Ryan chooses 6 numbers, then the probability that none of Ryan’s choices were drawn:-[tex]P(0)=^6C_0(0.025})^0(1-0.025)^{6}=(0.975)^6\approx0.8591[/tex]Hence, probability that none of Ryan’s choices were drawn = 0.8591