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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

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

Source: Magoosh

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Source: Beat The GMAT — Data Sufficiency | Tue Jun 18, 2019 11:17 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

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

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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