Question

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.

Answer 1

Answer: 0.8591

Step-by-step explanation:

Given : Total numbers in the jackpot : 40

Then the probability of getting jackpot = $\dfrac{1}{40}=0.025$

Using binomial probability formula :-

$P(x)=^nC_xp^x(1-p)^{n-x}$

If Ryan chooses 6 numbers, then the probability that none of Ryan’s choices were drawn:-

$P(0)=^6C_0(0.025})^0(1-0.025)^{6}=(0.975)^6\approx0.8591$

Hence,  probability that none of Ryan’s choices were drawn = 0.8591