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Vladimir [108]
3 years ago
12

In a​ lottery, the top cash prize was ​$642 ​million, going to three lucky winners. Players pick five different numbers from 1 t

o 53 and one number from 1 to 46. A player wins a minimum award of $400 by correctly matching two numbers drawn from the white balls​ (1 through 53​) and matching the number on the gold ball​ (1 through 46​). What is the probability of winning the minimum​ award?
Mathematics
1 answer:
kramer3 years ago
4 0

Answer:

\frac{10}{53 \times 46 \times 26}

Step-by-step explanation:

The probability of matching the number drawn on the gold ball is

\frac{1}{46}

The number of possible pairs of numbers from 1 to 53 is

\binom{53}{2}  =  \frac{53 \times 52}{2}  = 53 \times 26

Choosing 5 numbers, you are choosing 10 different pairs:

\binom{5}{2}  =  \frac{5 \times 4}{2}  = 10

Therefore the probability of correctly matching the drawn pair is

\frac{10}{53 \times 26}

Thus, the probability of winning (matching the pair AND the gold ball) is

\frac{10}{53 \times 46 \times 26}

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