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forsale [732]
3 years ago
6

Suppose that 5 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 5 are not black?

Mathematics
1 answer:
lions [1.4K]3 years ago
6 0
Here's the way I see it:  5 cards are drawn, one by one, without replacement.  Half (or 26) of the original deck are black and half (26) are white.

P(5 are not black) = P(5 are red)

P(5 are not black) = P(first card is red) * P(second card is red) * P(third card is red)*P(fourth card is red)*P(fifth card is red) =

(26/52) * (25/51) * (24/50) * (23/49) * (22/48) = 0.025   (answer)

We start with 52 cards.  We draw one, leaving 51 cards, 25 of which are red.  And so on.
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3 years ago
Sally works at a frozen yogurt shop that has about 2,500 customers per week and wants to know how many people like vanilla froze
Free_Kalibri [48]

Answer: The difference is 300 customers.

Step-by-step explanation:

For each week the proportion of customers that like vanilla frozen yogurt is equal to the number of customers that said they like it, divided by the sample (40 for each week)

week 1: p1 = 14/40 = 0.35

week 2: p2 = 18/40 = 0.45

week 3: p3 = 12/40 = 0.3

Then we can calculate the average proportion as:

P = (p1 + p2 + p3)/3 = 0.367

Now, knowing that in a week the shop has about 2500 customers, we can expect that 36.7% of them like the vanilla frozen yogurt,

This is:

N = 2500*0.367 = 916.6

But we can not have a 0.6 of a customer, so we should round it to the nearest whole number, which is 917.

Now, the standard deviation of this will be:

S = \sqrt{\frac{(0.300 - 0.367)^2 + (0.350 - 0.367)^2 + (0.450 - 0.367)^2}{2}}

wich is the summation of the squared difference with the mean of each value, divided by the number of repetitions minus one (3 - 1 = 2)

S = 0.075

Then the largest proportion is equal to the mean plus the standard deviation (P + S), and the smallest proportion is equal to the mean minus the standard deviation (P - S):

if we want to calculate the difference between those estimations, we need to calculate:

Diff = (P + S)*2500 - (P - S)*2500 = 2*S*2500 = 2*0.075*2500 = 300

So between the lower and the higher estimations, the difference is 300 customers.

8 0
3 years ago
Read 2 more answers
Find the median of the data in the box plot below
Ivan
It's the line that splits in the box part of the box plot
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