Please show all work and which probability distibution used! thanksS (Little bit

Question

Please show all work and which probability distibution used! thanksS

(Little bit challenging) Probability of winning a price from a randomly bought ‘Florida lottery’ ticket is 0.02. (This does not mean the grand price, it could be any price.) Gambler buys tickets and checks until he gets two winning tickets.

a)What is the probability of winning two prices price within first four attempts?

b)What is the probability of winning one price within first 3 attempts and winning second one within 4 to 6 attempts?

Explanation / Answer

Probability of winning a prize = 0.02

=> Probability of not winning a prize = 1 - 0.02 = 0.98

a) The probability of not winning a prize in first four attempts = 0.984 = 0.9224.

The probability of winning only one prize in first four attempts = 0.983 * 0.02 * 4 = 0.0753.

=> Probability of not winning two prizes in first four attempts = 0.9224 + 0.0753 = 0.9977.

=> Probability of winning two prizes in first four attempts = 1 - 0.9977 = 0.0023.

b) Probability of winning one prize in first 3 attempts = 3 * 0.02 * 0.982 = 0.0576.

Probability of winning one prize from 4th to 6th attempts = 0.0576.

=> Probability of both events happening = 0.0576 * 0.0576 = 0.0033.

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