Probability and Coin Flip

[dtweah]

Out of 100 Coins, one has heads on both sides ( A two-headed Coin). One coin is chosen at random and flipped two times. What is the probability of gettng two heads?

A. 1/4

B. 1/5

C. 101/400

D. 102/400

E. 103/400

[DeepakR]

Prob of getting 2 heads = P(getting 2 heads from normal coin) + P(getting 2 heads from 2headed coin)

We are selecting a normal coin from 100 coins = 100C1=100

P(getting 2H by flipping normal coin twice) = (1/2 * 1/2)/(100)=1/400

Selecting a 2Headed coin from 100 coins = 1

P(getting 2H from 2Headed coin)=(1/4)/1=1/4

P=1/400 + 1/4= 101/400 = C.)

-Deepak

[dumb.doofus]

I think its E i.e. 103/400

Steps:

There are two conditions. When you select a coin, it may be a normal coin or the other one that has two heads.

1. Abnormal Coin:
Probability of choosing the abnormal coin = 1/100
Probability of getting two heads on two flips = 1
So total probability of choosing the abnormal coin and getting two heads in two flips = 1*(1/100) = 1/100 ------- (1)

2. Normal Coin:
Probability of choosing the normal coin = 99/100
Probability of getting two heads on two flips = 1/4 (coz there are just 4 possibilities i.e. HH, TH, HT, TT)
So total probabiity of choosing the normal coin and getting two heads in two flips = (1/4)*(99/100) = 99/400 ------- (2)

So total probability of selecting any coin from those hundred coins and getting two heads in two flips = (1) + (2)
= 103/400