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We are asked to find the probability of getting exactly 2 heads in 3 coin tosses. Assuming the coin is fair, the probability of heads (p) = 0.5 and the probability of tails (q) = 0.5. Each toss is independent. This is a binomial probability problem, where: n = number of trials = 3 k = number of desired successes (heads) = 2 p = probability of success = 0.5 q = probability of failure = 0.5 The binomial probability formula is: 𝑃(𝑘 heads in 𝑛 tosses)=(𝑛𝑘)⋅𝑝𝑘⋅𝑞𝑛−𝑘 Plugging in the values: 𝑃(2 heads in 3 tosses)=(32)⋅(0.5)2⋅(0.5)1=3⋅0.25⋅0.5=0.375 Final Answer: The probability of getting exactly 2 heads in 3 coin tosses is 0.375 or 37.5%.
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- Primary
- Secondary
- WASSCE
- +9
levels :
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Secondary
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National Common Entrance Examination (NCEE)
GCE
Adult education
Undergraduate
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English
The probability of getting exactly \(2\) heads in \(3\) coin tosses is \(0.375\). We are asked to find the probability of getting exactly 2 heads in 3 coin tosses. Assuming the coin is fair, the probability of heads (p) = 0.5 and the probability of tails (q) = 0.5. Each toss is independent. This is a binomial probability problem, where: n = number of trials = 3 k = number of desired successes (heads) = 2 p = probability of success = 0.5 q = probability of failure = 0.5 The binomial probability formula is: 𝑃(𝑘 heads in 𝑛 tosses)=(𝑛𝑘)⋅𝑝𝑘⋅𝑞𝑛−𝑘 Plugging in the values: 𝑃(2 heads in 3 tosses)=(32)⋅(0.5)2⋅(0.5)1=3⋅0.25⋅0.5=0.375 Final Answer: The probability of getting exactly 2 heads in 3 coin tosses is 0.375 or 37.5%.
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