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Ganezh [65]
3 years ago
7

A drawer contains 6 black neckties, 2 white neckties,4 red neckties,2 maroon neckties and 2 blue neckties. One necktie is picked

at random and then replaced. This is repeated 300 times. Predict how many times you can expect the color of the necktie to be: A. White B. Blue C. Red D. Black E. Maroon F. Not white
Mathematics
1 answer:
kogti [31]3 years ago
4 0

A) The probability of picking a white tie 300 times = (\frac{1}{8}) ^{300}

B)  The probability of picking a blue tie 300 times = (\frac{1}{8}) ^{300}

C) The probability of picking a red tie 300 times = (\frac{1}{4}) ^{300}

D) the probability of picking a black tie 300 times = (\frac{3}{8}) ^{300}

E ) the probability of picking a maroon tie 300 times = (\frac{1}{8}) ^{300}

F) the probability of NOT picking a white tie 300 times = (\frac{7}{8}) ^{300}

Step-by-step explanation:

Here, the total number of black neckties  = 6

The total number of white neckties  = 2

The total number of red neckties  = 4

The total number of maroon neckties  = 2

The total number of blue neckties  = 2

The number of times the experiment is repeated = 300

A )  P(Picking a white tie)  = \frac{\textrm{Total number of white ties}}{\textrm{Total Bow ties}}

= \frac{2}{16}  = \frac{1}{8}

So, the probability of picking a white ONCE is 1/8.

Now, as the experiment is REPEATED 300 times with replacement.

So, the probability of picking a white tie 300 times = (\frac{1}{8}) ^{300}

B) P(Picking a BLUE  tie)  = \frac{\textrm{Total number of blue ties}}{\textrm{Total Bow ties}} = \frac{2}{16}  = \frac{1}{8}

So, the probability of picking a blue ONCE is 1/8.

Hence, the probability of picking a blue tie 300 times = (\frac{1}{8}) ^{300}

C) P(Picking a Red  tie)  = \frac{\textrm{Total number of Red ties}}{\textrm{Total Bow ties}} = \frac{4}{16}  = \frac{1}{4}

So, the probability of picking a red ONCE is 1/4.

Hence, the probability of picking a red tie 300 times = (\frac{1}{4}) ^{300}

D) P(Picking a Black  tie)  = \frac{\textrm{Total number of black ties}}{\textrm{Total Bow ties}} = \frac{6}{16}  = \frac{3}{8}

So, the probability of picking a red ONCE is 3/8.

Hence, the probability of picking a black tie 300 times = (\frac{3}{8}) ^{300}

E) P(Picking a maroon  tie)  = \frac{\textrm{Total number of maroon ties}}{\textrm{Total Bow ties}} = \frac{2}{16}  = \frac{1}{8}

So, the probability of picking a maroon ONCE is 1/8.

Hence, the probability of picking a maroon tie 300 times = (\frac{1}{8}) ^{300}

F) P(Picking a NOT whiten  tie)  = 1 - P( picking a white tie)

= 1-(\frac{1}{8} ) = \frac{8-1}{8}  = (\frac{7}{8} )

So, the probability of NOT  picking a white ONCE is 7/8.

Hence, the probability of NOT picking a white tie 300 times = (\frac{7}{8}) ^{300}

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