Probability-_1 @ dvhtlbz的部落格

標題:

Probability?

發問:

2 biased coins are tossed H T Find P(exactly 1H | at least 1H) Coin1 Prob 0.492 0.508 Find P(exactly 1T | at least 1T) Coin2 Prob 0.579 0.421 Also, please advise how you calculate it,Thank you!

最佳解答:

Let P( X , Y ) denote P( Coin 1 tossed X , Coin 2 tossed Y ) P( H H ) = 0.492*0.579 = 0.284868 P( H T ) = 0.492*0.421 = 0.207132 P( T H ) = 0.508*0.579 = 0.294132 P( T T ) = 0.508*0.421 = 0.213868 (1) P( exactly 1H | at least 1H ) = P( exactly 1H ∩ at least 1H ) / P( at least 1H ) = P( exactly 1H ) / P( at least 1H ) = [ P( H T ) + P( T H ) ] / [ P( H H ) + P( H T ) + P( T H ) ] = ( 0.207132 + 0.294132 ) / ( 0.284868 + 0.207132 + 0.294132 ) ≒ 0.638 ..... Ans (2) P( exactly 1T | at least 1T ) = P( exactly 1T ∩ at least 1T ) / P( at least 1T ) = P( exactly 1T ) / P( at least 1T ) = [ P( H T ) + P( T H ) ] / [ P( H T ) + P( T H ) + P( T T ) ] = ( 0.207132 + 0.294132 ) / ( 0.207132 + 0.294132 + 0.213868 ) ≒ 0.701 ..... Ans