In a toss of three coins together find [BT-4, CO-4, PO-2]
(i) the probability of getting atleast one head
(ii) the probability of getting atleast two head
(iii) the probability of getting atmost one head
(iv) the probability of getting atmost two head
(v) the cumulative distribution function.

We are tossing three coins together, so each coin has two possible outcomes: Head (H) or Tail (T). The total number of possible outcomes for three coins is \( 2^3 = 8 \).

Let's first list all the possible outcomes of tossing three coins:

\[
\text{Outcomes} = \{ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT \}
\]

### (i) Probability of getting at least one head

The event "at least one head" means getting one or more heads. The only outcome where there are no heads is \( TTT \).

So, the favorable outcomes are:
\[
\{ HHH, HHT, HTH, HTT, THH, THT, TTH \}
\]

There are 7 favorable outcomes, so the probability is:
\[
P(\text{at least one head}) = \frac{7}{8}
\]

### (ii) Probability of getting at least two heads

The event "at least two heads" means getting two or three heads. The favorable outcomes for this event are:
\[
\{ HHH, HHT, HTH, THH \}
\]

There are 4 favorable outcomes, so the probability is:
\

In a toss of three coins together find (i) the probability of getting atleast one head (ii) the probability of getting atleast two heads (iii) the probability of getting atmost one head (iv) the probability of getting atmost two heads (v) the cumulative distribution function.

Explore the probabilities of getting at least one head, at least two heads, at most one head, and at most two heads when tossing three coins together. This problem involves core concepts in probability theory, including favorable outcomes and the cumulative distribution function (CDF). Suitable for high school students (Grades 9-12).

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