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 .
Let's first list all the possible outcomes of tossing three coins:
(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 .
So, the favorable outcomes are:
There are 7 favorable outcomes, so the probability is:
(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:
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
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