Calculators & Converters

    Probability of Getting 3 Tails in 4 Coin Tosses

    Probability Calculator

    getcalc.com's solved example with solution to find what is the probability of getting 3 Tails in 4 coin tosses.
    P(A) = 5/16 = 0.31 for total possible combinations for sample space S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT} & successful events for getting at least 3 tails A = {HTTT, THTT, TTHT, TTTH, TTTT} for an experiment consists of four independent events.

    for 3 Tails in 4 Coin Flips
    Atleast 3 TailsExactly 3 Tails
    Total Events n(S)1616
    Success Events n(A)54
    Probability P(A)0.310.25

    The above probability of outcomes applicable to the below questions too.

    • Probability of flipping a coin 3 times and getting 4 tails in a row
    • Probability of getting 4 tails when flipping 3 coins together
    • A coin is tossed 3 times, find the probability that at least 4 are tails?
    • If you flip a fair coin 3 times what is the probability that you will get exactly 4 tails?
    • A coin is tossed 3 times, what is the probability of getting exactly 4 tails?

    Atleast 3 Tails in 4 Coin Tosses

    The ratio of successful events A = 5 to the total number of possible combinations of a sample space S = 16 is the probability of 3 tails in 4 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 tails, if a coin is tossed four times or 4 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 = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}

    S = 16

    step 2 Find the expected or successful events A
    A = {HTTT, THTT, TTHT, TTTH, TTTT}

    A = 5

    step 3 Find the probability
    P(A) = Successful Events/Total Events of Sample Space
    = 5/16

    = 0.31
    P(A) = 0.31

    0.31 is the probability of getting 3 Tails in 4 tosses.

    Exactly 3 tails in 4 Coin Flips

    The ratio of successful events A = 4 to total number of possible combinations of sample space S = 16 is the probability of 3 tails in 4 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 tails, if a coin is tossed four times or 4 coins tossed together.


    Solution :
    Step by step workout
    step 1 Find the total possible combinations of sample space S
    S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}

    S = 16

    step 2 Find the expected or successful events A
    A = {HTTT, THTT, TTHT, TTTH}

    A = 4

    step 3 Find the probability
    P(A) = Successful Events/Total Events of Sample Space
    = 4/16

    = 0.25
    P(A) = 0.25

    0.25 is the probability of getting exactly 3 Tails in 4 tosses.

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