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10 Jan 2021, 11:15
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B
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A box contains three coins, two of them are fair and the third is two-headed. A coin is selected at random and tossed. If heads appears, the coin is tossed again. If tails appears, then another coin is selected from the two remaining coins and tossed. If the same coin is tossed twice, what is the probability that it is the two-headed coin?
A. 2/3
B. 1/2
C. 3/8
D. 1/4
E. 1/8
Are You Up For the Challenge: 700 Level Questions
A. 2/3
B. 1/2
C. 3/8
D. 1/4
E. 1/8
Are You Up For the Challenge: 700 Level Questions
10 Nov 2021, 06:12
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The important thing to note here is : the same coin is tossed twice ie, we are not concerned with the outcome of 2nd toss...only 1st should be heads.
1st heads can come in 2 ways ...if 2 fair coins are chosen and both render heads + unfair coin is chosen:
Case 1: Fair coin: 2/3 * 1/2 = 1/3 (2/3 -- prob. of choosing 2 Fair coin, 1/2 - 1st toss heads)
Case 2: unfair coin: 1/3 *1 = 1/3 (1/3 -- prob. of choosing unfair coin, 1 - 1st toss heads)
P = unfair / total
P = 1/3 / (1/3+1/3) = 1/2
B
1st heads can come in 2 ways ...if 2 fair coins are chosen and both render heads + unfair coin is chosen:
Case 1: Fair coin: 2/3 * 1/2 = 1/3 (2/3 -- prob. of choosing 2 Fair coin, 1/2 - 1st toss heads)
Case 2: unfair coin: 1/3 *1 = 1/3 (1/3 -- prob. of choosing unfair coin, 1 - 1st toss heads)
P = unfair / total
P = 1/3 / (1/3+1/3) = 1/2
B
General Discussion
Deepakjhamb
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10 Jan 2021, 11:46
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p (same coin tossed ) * p( 2headed coin /same coin tossed) = p( same coin tossed and 2 head coin)
p(same coin tossed ) = 2/3 *1/2 *1 + 1/3 *1*1 = 1/6+1/3 = 1/2
p(same coin tossed and 2 headed coin) = 1/3 *1 *1 =1/3
p( 2headed coin /same coin tossed) = 1/3/(1/2) = 2/3
so answer is a)2/3
p(same coin tossed ) = 2/3 *1/2 *1 + 1/3 *1*1 = 1/6+1/3 = 1/2
p(same coin tossed and 2 headed coin) = 1/3 *1 *1 =1/3
p( 2headed coin /same coin tossed) = 1/3/(1/2) = 2/3
so answer is a)2/3
