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A weighted coin has a probability p of showing heads. Is the

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A weighted coin has a probability p of showing heads. Is the

by BTGmoderatorDC » Tue Jun 18, 2019 11:17 pm

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A weighted coin has a probability p of showing heads. Is the value of p > 0.2?


(1) Successive flips are independent, and the probability of getting at least one head in two flips is greater than 0.5.

(2) The probability of getting tail on a flip of coin is less than 0.8.

OA D

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by deloitte247 » Sat Jun 29, 2019 10:26 am

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Is the value of P > 0.2 ?
Statement 1
Successful flips are independent and the probability of getting at least one head in the flip is < 0.5
Probability of two tails is < 0.5
$$\left(1-p\right)\left(1-p\right)<0.5$$
$$\left(1-p\right)^2<0.5$$
$$\sqrt{\left(1-p\right)^2}<\sqrt{0.5}$$
$$1-p=0.707$$
$$-p=0.707-1$$
$$p>0.293$$
$$statement\ 1\ \ is\ SUFFICIENT.$$

Statement 2
The probability of getting a tail on a flip of coin is less than 0.8
$$1-p<0.8$$
$$-p>-0.2$$
$$p>0.2$$ $$Statement\ 2\ is\ \ INSUFFICIENT$$
Each statement alone is SUFFICIENT.

$$answer\ is\ Option\ D$$
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