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1) You take the four Aces, four 2's, and four 3's from a standard deck of 52 cards, forming a set of 12 cards. You then deal all 12 cards at random to four players, so that each player gets three cards. What is the probability that each player gets an Ace, a 2, and a 3?

 

2) In a Lottery, three balls are drawn (at random) from ten white balls numbered from 1 to 10, and one LotteryBall is drawn (at random) from ten red balls numbered from 11 to 20. When you buy a ticket, you choose three numbers from 1 to 10 and one number from 11 to 20.

If the numbers on your ticket match at least two of the white balls or match the red LotteryBall, then you win a super prize. What is the probability that you win a super prize?

 Apr 23, 2020
 #1
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1)  I'm going to deal to player A all of this player's cards first:

     ---   it doesn't matter what this player gets on the first card:              12/12

     ---  there are 8 cards remaining that don't match the first card:           8/11

     ---  there are 4 cards remaining that don't match the first two cards:   4/10

     Now, for player B:

     ---  it doesn't matter what this player gets on the first card:                  9/9

     ---  there are 6 cards remaining that don't match the first card:            6/8

     --- there are 3 cards remaining that don't match the first two cards:    3/7

     Now, for player C:

     ---  it doesn't matter what this player gets on the first card:                  6/6

     ---  there are 4 cards remaining that don't match the first card:            4/5

     ---  there are 2 cards remaining that don't match the first two cards:   2/4

    Now, for player D:

    ---  it doesn't matter what this player gets on the first card:                   3/3

    ---  it doesn't matter what this player gets on the second card:             2/2

    ---  there is only one card left:                                                               1/1

 

Multiplying these together:  0.0374

 Apr 23, 2020

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