Calculators & Converters

    Probability of Getting 3 Heads in 5 Coin Tosses

    Probability Calculator

    getcalc.com's solved example with solution to find what is the probability of getting 3 Heads in 5 coin tosses.

    P(A) = 16/32 = 0.5

    for 3 Heads in 5 Coin Flips
    Atleast 3 HeadsExactly 3 Heads
    Total Events n(S)3232
    Success Events n(A)1610
    Probability P(A)0.50.31

    Atleast 3 Heads in 5 Coin Tosses

    The ratio of successful events A = 16 to the total number of possible combinations of a sample space S = 32 is the probability of 3 heads in 5 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 five times or 5 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 = {HHHHH, HHHHT, HHHTH, HHHTT, HHTHH, HHTHT, HHTTH, HHTTT, HTHHH, HTHHT, HTHTH, HTHTT, HTTHH, HTTHT, HTTTH, HTTTT, THHHH, THHHT, THHTH, THHTT, THTHH, THTHT, THTTH, THTTT, TTHHH, TTHHT, TTHTH, TTHTT, TTTHH, TTTHT, TTTTH, TTTTT}

    S = 32

    step 2 Find the expected or successful events A
    A = {HHHHH, HHHHT, HHHTH, HHHTT, HHTHH, HHTHT, HHTTH, HTHHH, HTHHT, HTHTH, HTTHH, THHHH, THHHT, THHTH, THTHH, TTHHH}

    A = 16

    step 3 Find the probability
    P(A) = Successful Events/Total Events of Sample Space
    = 16/32

    = 0.5
    P(A) = 0.5

    0.5 is the probability of getting 3 Heads in 5 tosses.

    Exactly 3 heads in 5 Coin Flips

    The ratio of successful events A = 10 to total number of possible combinations of sample space S = 32 is the probability of 3 heads in 5 coin tosses. Users may refer the below detailed solved example with step by step calculation to learn how to find what is the probability of getting exactly 3 heads, if a coin is tossed five times or 5 coins tossed together.


    Solution :
    Step by step workout
    step 1 Find the total possible combinations of sample space S
    S = {HHHHH, HHHHT, HHHTH, HHHTT, HHTHH, HHTHT, HHTTH, HHTTT, HTHHH, HTHHT, HTHTH, HTHTT, HTTHH, HTTHT, HTTTH, HTTTT, THHHH, THHHT, THHTH, THHTT, THTHH, THTHT, THTTH, THTTT, TTHHH, TTHHT, TTHTH, TTHTT, TTTHH, TTTHT, TTTTH, TTTTT}

    S = 32

    step 2 Find the expected or successful events A
    A = {HHHTT, HHTHT, HHTTH, HTHHT, HTHTH, HTTHH, THHHT, THHTH, THTHH, TTHHH}

    A = 10

    step 3 Find the probability
    P(A) = Successful Events/Total Events of Sample Space
    = 10/32

    = 0.31
    P(A) = 0.31

    0.31 is the probability of getting exactly 3 Heads in 5 tosses.

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