Posted by Elizabeth on Saturday, December 5, 2009 at 4:29pm.
When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below:
HHHH HHHT HHTH HHTT
HTHH HTHT HTTH HTTT
THHH THHT THTH THTT
TTHH TTHT TTTH TTTT
Let X denote the total number of tails obtained in the four tosses. Find the probability distribution of the random variable X. Leave your probabilities in fraction form.
math - MathMate, Sunday, December 6, 2009 at 11:07am
As you mentioned, there are 16 possible outcomes each with equal probability.
For X=0, there is only one case out of sixteen, namely HHHH. Therefore
For X=1, you will count the number of cases where T occurs only once. You should count 4 of such cases, therefore
Repeat the calculation for X=2,3,4 and obtain the values of X(2), X(3), and X(4).
The sum of the values X(0) to X(5) should equal to 1.
math - PsyDAG, Sunday, December 6, 2009 at 11:10am
If there are 16 possible outcomes for the 4 tosses, the probability of getting 4 tails = 1/16, 3 tails = 4/16 = 1/4, 2 tails = ?, 1 tail = ?, no tails = ?.
I'll let you calculate the remaining fractions.
As a check, the sum of these fractions must = 1.
I hope this helps.
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