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makvit [3.9K]
3 years ago
5

Three cards are drawn sequentially from a shuffled deck without replacement. What is the approximate probability all three drawn

cards have NUMBERS on them?
Mathematics
1 answer:
bekas [8.4K]3 years ago
8 0

Answer:

Step-by-step explanation:

There are 36 numbered cards out of 52 total cards .

so in the first attempt probability of numbered cards being drawn

= 36 / 52

After first draw , numbered cards remaining = 35 , total no of card remaining = 51

probability of numbered card  in 2nd attempt = 35 / 51

Probability in third attempt

= 34 / 50

Total probability  of all cards being numbers = (36 / 52) x (35 / 51) x (34/50)

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Answer:

Step-by-step explanation:

Let's use binomial distribution, because we are interested in find the total number of successes in a sequence of n independent experiments.

In probability, a binomial distribution is used in a Bernoulli process. That is, a sequence of experiments of n independent  trials, each asking a dichotomous question, that means it only has two answers. One answer is a success (probability: p) and the other is a failure (probability: 1-p). In this case, every customer who enters in the store is the experiment. If they make a purchase is a success event, taking into account that every purchase decision has to be independent.

P(X=x) = C(n,x)p^{x} (1-p)^{n-x}

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a) x= 5 ------> customers that make a purchase

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p=0.3

p(X=5)= C(6,5)(0.3)^{5} (1-0.3)^{6-5} \\p(X=5)=0.102

b) At least 3 customers make a purchase. x ≥ 3

P(X\geq 3)=1-P (X=0)-P(X=1)-P(X=2)\\P(X\geq 3)=1-(C(6,0)(0.3^{0})(0.7)^{6}) - (C(6,1)(0.3^{1})(0.7)^{5}) - (C(6,2)(0.3^{2})(0.7)^{4})\\ P(X\geq 3) = 1-0.11765-0.30253-0.32414\\P(X\geq3)= 0.2557

c) At most 2 customers make a purchase. x ≤ 2

P(X\leq2) = P(X=0) + P(X=1) + P(X=2)\\P(X\leq2) = (C(6,0)(0.3^{0})(0.7)^{6}) + (C(6,1)(0.3^{1})(0.7)^{5}) + (C(6,2)(0.3^{2})(0.7)^{4})\\P(X\leq2) = 0.11765-0.30253-0.32414\\P(X\leq2)=0.7443

d)At least 1 customer makes a purchase. x ≥ 1

P(X\geq 1)=1-P(X=0)\\P(X\geq 1)= 1-C(0,6)(0.3)^{0}(0.7)^{6} \\P(X\geq 1)= 1-0.11765 = 0.8824

e)They must be kind to customers, always willing to help and give information about products clearly and honestly.

Have enough inventory and offer promotions for the purchase of more than one product

Have an agile payment system that avoids rows and delays in purchases.

6 0
3 years ago
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