The game called Lotto sponsored by the Louisiana Lottery Commission pays its lar

Question

The game called Lotto sponsored by the Louisiana Lottery Commission pays its largest prize when a contestant matches all 6 of the 44 possible numbers. Assume there are 44 ping-pong balls each with a single number between 1 and 44. Any number appears only once, and the winning balls are selected without replacement. b. Use the hypergeometric formula to find the probability of matching all 6 winning numbers. The lottery commission also pays if a contestant matches 4 or 5 of the 6 winning numbers. Hint: Divide the 44 numbers into two groups, winning numbers and nonwinning numbers. (Round your answer to 8 decimal places.) Probability c. Find the probability, again using the hypergeometric formula, for matching 4 of the 6 winning numbers. (Round your answer to 8 decimal places.) Probability d. Find the probability of matching 5 of the 6 winning numbers. (Round your answer to 8 decimal places.) Probability

Explanation / Answer

there are all total 44 ping pong balls. out of which 6 are winning numbers and 44-6=38 are non winning numbers.

6 ping pong balls are selected at random without replacement.

let X denotes the number of winning ping pong balls out of 6 balls selected.

so X~Hypergeometric(44,38,6)

P[X=x]=6Cx*38C6-x/44C6

b.) hence probability of matching all 6 winning numbers is

P[X=6]=6C6*38C0/44C6=0.00000014 [answer]

c) probability of matching 4 of the 6 winning numbers is

P[X=4]=6C4*38C2/44C6=0.00149383 [answer]

d) probability of matching 5 of the 6 winning numbers is

P[X=5]=6C5*38C1/44C6=0.00003230 [answer]

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