Question

Suppose that we are interested I the number of heads showing face up on three tosses of a coin. This is the experiment. The possible results are: zero heads, one head, two heads, and three heads. What is the probability distribution for the number of heads?

In a region of a country, 5% of all cell phone calls are dropped. What is the probability that out of six randomly selected calls, none was dropped? Exactly one? Exactly two ? exactly three? Exactly four? Exactly five? Exactly six out of six

Suppose that we are interested I the number of heads showing face up on three tosses of a coin. This is the experiment. The possible results are: zero heads, one head, two heads, and three heads. What is the probability distribution for the number of heads?

Answer 1

The sample space of a fair coin flip is {H, T}
The sample space of a sequence of three fair coin flips is all 2³ possible sequences of outcomes:
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Then, let us calculate the different probabilities:

Thus the probability distribution is given by

Number of heads	zero heads	one head	two heads	three heads
Probability	1/8	3/8	3/8	1/8

Now, for the next question: In a region of a country, 5% of all cell phone calls are dropped. So, probability of a cell phone call being dropped = 5% = 0.05, thus probability of a call not being dropped = 1 - 0.05 = 0.95

Thus, we can use this to calculate the required probabilities for a sample of six randomly selected calls.