If you buy 1 ticket in canada's lotto 6/49 lottery game, the probability that you will win a prize is 0.15. Given the nature of lotteries, the probability of winning is independent from month to month. If you buy 1 ticket each month for five months, what is the probability that you will win at least one prize?

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fichoh fichoh · Answer 1 · 2020-12-01T04:57:57+01:00

Answer:

0.5563

Step-by-step explanation:

Given that :

Probability of winning (p) = 0.15

Number of months = number of trials (n) = 5

1 - p = 1 - 0.15 = 0.85

Probability of winning atleast one price ;

P(x = x) = nCx * p^x * (1 - p)^(n-x)

P(x≥1) = p(1) + p(2) + p(3) + p(4) + p(5)

Using the binomial probability calculator to save computation time :

P(x≥1) = 0.556294

P(x≥1) = 0.5563

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MrRoyal MrRoyal · Answer 2 · 2021-12-10T13:11:23+01:00

Probabilities are used to determine the chances of events.

The probability that you win at least one prize is 0.5563

The given parameters are:

[tex]p = 0.15[/tex] --- the probability of winning

The probability of losing (q) is then calculated using the following complement rule

[tex]q= 1 - p[/tex]

[tex]q= 1 - 0.15[/tex]

[tex]q= 0.85[/tex]

The probability that you win at least one prize is the complement of not winning at all.

So, we have:

[tex]P(At\ least\ 1) = 1 - P(None)[/tex]

This gives

[tex]P(At\ least\ 1) = 1 - 0.85^5[/tex]

[tex]P(At\ least\ 1) = 1 - 0.4437[/tex]

Evaluate like terms

[tex]P(At\ least\ 1) = 0.5563[/tex]

Hence, the probability of winning at least one prize is 0.5563