If you buy one ticket in the provincial lottery, then the probability that you will win a prize is 0.11. given the nature of lotteries, the probability of winning is independent from month to month. if you buy one ticket each month for five months, what is the probability that you will win at least one prize?

Given that the probability that you will win a prize in the provincial lottery is 0.11.

If you buy one ticket each month for five months, the probability that you will win at least one prize is given by

[tex]P(x\geq1)=1-P(x\ \textless \ 1) \\ \\ =1-P(0)=1-{ ^5C_0(0.11)^0(1-0.11)^5} \\ \\ =1-1\times1\times(0.89)^5=1-0.5584=0.4416[/tex]

Therefore, the probability that you will win at least one prize is 0.4416 or 44.16%.

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divyamadaan8054 divyamadaan8054 · Answer 2 · 2021-10-12T09:01:08+02:00

Answer:

The probability of winning at least one prize is [tex]0.4416[/tex] or [tex]44.16\%[/tex].

Step-by-step explanation:

Given: If you buy one ticket in the provincial lottery, then the probability that you will win a prize is [tex]0.11[/tex] and the nature of lotteries, the probability of winning is independent from month to month.

According to question,

Probability of winning atleast one prize by buying one ticket each month for five months is formulated as [tex]P(X\geq 1)=1-P(x<1)[/tex].

Now, using Binomial distribution formula:

The binomial distribution formula is for any random variable [tex]X[/tex], given by; [tex]p\left ( x:n,p \right )=^{n}{{C}_{r}}p^x\left ( 1-p \right )^{n-x}[/tex]

[tex]P(X\geq 1)=1-P(x<1)\\[/tex]

[tex]= 1-P(0)\\ = 1-^{5}{{C}_{0}}(0.11)^0\left ( 1-0.11 \right )^{5-0}\\ = 1-1\times1\times (0.89)^5\\ =1-0.5584\\ = 0.4416[/tex]

Hence, the probability that you will win at least one prize is [tex]0.4416[/tex].

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