Posted by **Shelagh** on Wednesday, June 18, 2014 at 7:30pm.

Four coins fall onto the floor. Find the probability that

(a) exactly three coins land heads up

(b) all coins land tails up

(c) two or more coins land heads up

(d) no more than two coins land tails up

(e) at least one coin lands tails up

- Math -
**MathMate**, Thursday, June 19, 2014 at 6:27am
Each coin can land heads or tails with equal probability of 1/2.

Dropping a coin four times has 2^4=16 possible outcomes.

(a) three heads

By enumeration:

There are four possible outcomes, so the probability is 4/16. THHH,HTHH,HHTH,HHHT.

The number of combinations for 3H can be calculated as 4C3=4!/((1!)(3!))

So probability = 4C3/16

If you are familiar with the binomial probability formula, then

P(3H)=4C3*(1/2)^3(1/2)^1

=4!/(1!3!)*(1/16)=4/16

(b) there can be only one outcome out of 16.

(c)Use enumeration, or combination to find 4C2+4C3+4C4

(d)(e) similar to above.

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