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CBSE Class 12-science Answered

Three cards are drawn sucessively with replacementfrom a well suffled deck of 52 cards. A random variable X denotes the number of hearts in the three cards drawn. Determine the probability distribution of X. Also find E(X).
Asked by mishrapragu1998 | 12 Mar, 2016, 09:38: AM
answered-by-expert Expert Answer
begin mathsize 12px style straight P open parentheses straight X equals 1 close parentheses equals fraction numerator 3 cross times 13 cross times 39 cross times 39 over denominator 52 cross times 52 cross times 52 end fraction space equals 27 over 64 Since space cards space are space drawn space with space replacement comma space every space time space we space have space 52 space cards space to space choose space from and space One space heart space can space be space picked space in space 13 space ways. space The space remaining space two space cards space can space be space picked space in space 39 space ways space each. Also comma space the space heart space card space can space be space either space the space first space one space or space the space second space one space or space the space third space one. space So space three space ways. Similarly space straight P open parentheses straight X equals 2 close parentheses equals space fraction numerator 3 cross times 13 cross times 13 cross times 39 over denominator 52 cross times 52 cross times 52 end fraction space equals 9 over 64 straight P open parentheses straight X equals 3 close parentheses equals fraction numerator 13 cross times 13 cross times 13 over denominator 52 cross times 52 cross times 52 end fraction equals 1 over 64 straight E open parentheses straight X close parentheses equals sum from straight X equals 1 to 3 of XP open parentheses straight X close parentheses equals 1 cross times 27 over 64 plus 2 cross times 9 over 64 plus 3 cross times 1 over 64 equals 48 over 64 equals 3 over 4 end style
Answered by satyajit samal | 14 Mar, 2016, 12:37: PM

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