2. (20) In the Rawdonville Lottery, five balls are chosen from an urn (without r

Question

2. (20) In the Rawdonville Lottery, five balls are chosen from an urn (without replacement) with the balls labeled 1 through 40. There is also a Slammin' Sammy ball which is chosen from a separate urn with balls labeled 1 through 13. You decide to play the lottery because it sounds like so much fun. So you choose five numbers between 1 and 40 and a Slammin' Sammy number between 1 and 13 (a) What is the probability of winning the Rawdonville Lottery (that is, getting al five numbers to match the draw and matching the Slammin' Sammy ball)? (b) What is the probability of having three of your five choices match the lottery draw while missing the Slammin' Sammy number?

Explanation / Answer

Similarly, the only way you can get the other ball correct in 1 way. But the ball can be picked in 13C1 ways. Hence probability=(1/40C5) *(1/13C1)

2. Basically you have to get 3 balls correct and 2 balls incorrect, which means you need to choose 3 out of 5 correct balls and 2 out of remaining 35 balls, but total no. of ways in which balls can be chosen is 40C5.

On the other hand, we dint get the other ball right, probability of which is 12C1/13C1

Hence, probability=( 5C3*35C2/40C5)*(12C1/13C1)

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