Chapter 11.7, Problem 31E

a.

To determine

To find the probability of holding both the winning tickets

Answer to Problem 31E

The probability of holding both winning tickets is $\frac{1}{1225}$

Explanation of Solution

Given information:

The given combinations is ${}_{50}{C}_2$

Calculation:

  $\begin{array}{l}{}_n{C}_r{=}_{50}{C}_2\\ {}_n{C}_r=\frac{n!}{r!\left(n-r\right)!}\text{ [Use combinations formula]}\\ {}_{50}{C}_2=\frac{50!}{2!(50-2)!}\\ {}_{50}{C}_2=\frac{50!}{2!\times 48!}=\frac{50\times 49\times 48}{2\times 48}\text{ [Divide out common]}\\ {}_{50}{C}_2=\frac{1}{1225}\text{ [Simplify}\text{.]}\end{array}$

b.

To determine

Does buying twice as many tickets double the probability of holding both winning tickets. Explain

Answer to Problem 31E

Yes, the probability will be increase probability.

Explanation of Solution

Given information:

If more tickets are bought, than the denominator will be reduces, thereby increasing the probability