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Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

coin problem?

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  • 2 months ago

    There are 8 possible outcomes.

    HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

    Just count the number of desired outcomes and divide by 8.

    PROBLEM 1:

    3 heads --> HHH

    P(3 heads) = 1/8

    PROBLEM 2:

    2 heads and 1 tail --> HHT, HTH, THH

    P(2 heads and 1 tail) = 3/8

    PROBLEM 3:

    At least one tail --> HHT, HTH, HTT, THH, THT, TTH, TTT

    P(at least one tail) = 7/8

     

    P.S. A faster way to figure this might be to think of the opposite case. If you don't toss at least one tail, it means you tossed all 3 heads. We know the probability of 3 heads is 1/8, so the probability of no heads (aka at least one tail) is:

    1 - 1/8

    = 7/8

    PROBLEM 4:

    At least two heads --> HHH, HHT, HTH, THH

    P(at least two heads) = 4/8 = 1/2

    P.S. The two cases we are considering are 3 heads (0 tails) and 2 heads (1 tail). But by symmetry, we could be counting the same thing for tails with 3 tails (0 heads) and 2 tails (1 head). These two probabilities will be exactly the same and that covers all the possible outcomes. As a result, each probability will be the same = 1/2.

    P.P.S. You could also add the results for part 1 and part 2.

    P(at least 2 heads) = P(3 heads) + P(2 heads)

    = 1/8 + 3/8

    = 4/8

    = 1/2

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  • 2 months ago

    1. 3 heads

    P( 3 heads) = 1/8   answer//

    2. 2 heads and tail

     P(2H and T) = 3/8  answer//

    3. At least 1 tail

     P(at least 1 tail) = 7/8 answer//

    3. At least 2 heads

    P(at least 2 heads) = 4/8 or 1/2  answer..//

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  • 2 months ago

    How do you toss an event?

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  • 2 months ago

    H: Head

    T: Tail

    P(H) = 1/2

    P(T) = 1/2

    ====

    1.

    P(3H)

    = P(H)³

    = (1/2)³

    = 1/8

    = 0.125

    ====

    2.

    Method 1:

    P(2H 1T)

    = P(HHT) + P(HTH) + P(THH)

    = (1/2)³ + (1/2)³ + (1/2)³

    = 3/8

    = 0.375

    Method 2:

    P(2H 1T)

    = ₃C₂ × (1/2)² × (1/2)

    = 3 × (1/4) × (1/2)

    = 3/8

    = 0.375

    ====

    3.

    P(at least 1T)

    = 1 - P(3T)

    = 1 - (1/2)³

    = 1 - (1/8)

    = 7/8

    = 0.875

    ====

    4.

    P(at least 2H)

    = P(2H 1T) + P(3H)

    = 0.375 + 0.125

    = 0.5

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