A coin is tossed 6 times, what is the probability of getting exactly 3 heads

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Text Solution

`(11)/( 16)``(21)/(32)``(1)/(18)``(3)/(64)`

Answer : B

Solution : In a single throw we have `P(H) =(1)/(2) ` and P (not H) =`(1)/(2)` <br> `:. , p =(1)/(2),q=(1)/(2) " and " n=6` <br> Required probability =P(3 heads or 4 heads or 5 heads or 6 heads ) <br> `=^(6)C_(3) .((1)/(2))^(3).((1)/(2))^(3)+.^(6)C_(4) .((1)/(2))^(4) .((1)/(2))^(2) +.^(6)C_(5).((1)/(2))^(5).((1)/(2)) +.^(6)C_(6).((1)/(2))^(6)` <br> `=(20 xx (1)/(64) +15 xx (1)/(64) +6xx (1)/(64) +(1)/(64)) =(42)/(64) =(21)/(32)`

The ratio of successful events A = 42 to the total number of possible combinations of a sample space S = 64 is the probability of 3 heads in 6 coin tosses. Users may refer the below solved example work with steps to learn how to find what is the probability of getting at-least 3 heads, if a coin is tossed fix times or 6 coins tossed together. Users may refer this tree diagram to learn how to find all the possible combinations of sample space for flipping a coin one, two, three or four times.

Solution

Step by step workout
step 1 Find the total possible events of sample space S S = {HHHHHH, HHHHHT, HHHHTH, HHHHTT, HHHTHH, HHHTHT, HHHTTH, HHHTTT, HHTHHH, HHTHHT, HHTHTH, HHTHTT, HHTTHH, HHTTHT, HHTTTH, HHTTTT, HTHHHH, HTHHHT, HTHHTH, HTHHTT, HTHTHH, HTHTHT, HTHTTH, HTHTTT, HTTHHH, HTTHHT, HTTHTH, HTTHTT, HTTTHH, HTTTHT, HTTTTH, HTTTTT, THHHHH, THHHHT, THHHTH, THHHTT, THHTHH, THHTHT, THHTTH, THHTTT, THTHHH, THTHHT, THTHTH, THTHTT, THTTHH, THTTHT, THTTTH, THTTTT, TTHHHH, TTHHHT, TTHHTH, TTHHTT, TTHTHH, TTHTHT, TTHTTH, TTHTTT, TTTHHH, TTTHHT, TTTHTH, TTTHTT, TTTTHH, TTTTHT, TTTTTH, TTTTTT} S = 64

step 2 Find the expected or successful events A

step 3 Find the probability

0.66 is the probability of getting 3 Heads in 6 tosses.