Math Problem Statement

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.

Solution

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 23=82^3 = 8.

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

Outcomes={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}\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 TTTTTT.

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

There are 7 favorable outcomes, so the probability is: P(at least one head)=78P(\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}\{ HHH, HHT, HTH, THH \}

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

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Math Problem Analysis

Mathematical Concepts

Probability
Coin Toss Experiment
Cumulative Distribution Function

Formulas

Probability formula: P(Event) = Number of favorable outcomes / Total number of outcomes
Cumulative Distribution Function (CDF)

Theorems

Basic Probability Theorem
Law of Total Probability

Suitable Grade Level

Grades 9-12